Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems

Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kashif Hussain [verfasserIn] Oluwaseun Adeyeye [verfasserIn] Nazihah Ahmad [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor

Übergeordnetes Werk:	In: International Islamic University Malaysia Engineering Journal - IIUM Press, International Islamic University Malaysia, 2015, 24(2023), 1
Übergeordnetes Werk:	volume:24 ; year:2023 ; number:1

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.31436/iiumej.v24i1.2380

Katalog-ID:	DOAJ08288935X

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allfields	10.31436/iiumej.v24i1.2380 doi (DE-627)DOAJ08288935X (DE-599)DOAJ297409832f0645688c8c2a174222e0e5 DE-627 ger DE-627 rakwb eng TA1-2040 Kashif Hussain verfasserin aut Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan. Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor Engineering (General). Civil engineering (General) Oluwaseun Adeyeye verfasserin aut Nazihah Ahmad verfasserin aut In International Islamic University Malaysia Engineering Journal IIUM Press, International Islamic University Malaysia, 2015 24(2023), 1 (DE-627)1010842064 22897860 nnns volume:24 year:2023 number:1 https://doi.org/10.31436/iiumej.v24i1.2380 kostenfrei https://doaj.org/article/297409832f0645688c8c2a174222e0e5 kostenfrei https://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/2380 kostenfrei https://doaj.org/toc/1511-788X Journal toc kostenfrei https://doaj.org/toc/2289-7860 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2023 1
spelling	10.31436/iiumej.v24i1.2380 doi (DE-627)DOAJ08288935X (DE-599)DOAJ297409832f0645688c8c2a174222e0e5 DE-627 ger DE-627 rakwb eng TA1-2040 Kashif Hussain verfasserin aut Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan. Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor Engineering (General). Civil engineering (General) Oluwaseun Adeyeye verfasserin aut Nazihah Ahmad verfasserin aut In International Islamic University Malaysia Engineering Journal IIUM Press, International Islamic University Malaysia, 2015 24(2023), 1 (DE-627)1010842064 22897860 nnns volume:24 year:2023 number:1 https://doi.org/10.31436/iiumej.v24i1.2380 kostenfrei https://doaj.org/article/297409832f0645688c8c2a174222e0e5 kostenfrei https://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/2380 kostenfrei https://doaj.org/toc/1511-788X Journal toc kostenfrei https://doaj.org/toc/2289-7860 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2023 1
allfields_unstemmed	10.31436/iiumej.v24i1.2380 doi (DE-627)DOAJ08288935X (DE-599)DOAJ297409832f0645688c8c2a174222e0e5 DE-627 ger DE-627 rakwb eng TA1-2040 Kashif Hussain verfasserin aut Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan. Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor Engineering (General). Civil engineering (General) Oluwaseun Adeyeye verfasserin aut Nazihah Ahmad verfasserin aut In International Islamic University Malaysia Engineering Journal IIUM Press, International Islamic University Malaysia, 2015 24(2023), 1 (DE-627)1010842064 22897860 nnns volume:24 year:2023 number:1 https://doi.org/10.31436/iiumej.v24i1.2380 kostenfrei https://doaj.org/article/297409832f0645688c8c2a174222e0e5 kostenfrei https://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/2380 kostenfrei https://doaj.org/toc/1511-788X Journal toc kostenfrei https://doaj.org/toc/2289-7860 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2023 1
allfieldsGer	10.31436/iiumej.v24i1.2380 doi (DE-627)DOAJ08288935X (DE-599)DOAJ297409832f0645688c8c2a174222e0e5 DE-627 ger DE-627 rakwb eng TA1-2040 Kashif Hussain verfasserin aut Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan. Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor Engineering (General). Civil engineering (General) Oluwaseun Adeyeye verfasserin aut Nazihah Ahmad verfasserin aut In International Islamic University Malaysia Engineering Journal IIUM Press, International Islamic University Malaysia, 2015 24(2023), 1 (DE-627)1010842064 22897860 nnns volume:24 year:2023 number:1 https://doi.org/10.31436/iiumej.v24i1.2380 kostenfrei https://doaj.org/article/297409832f0645688c8c2a174222e0e5 kostenfrei https://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/2380 kostenfrei https://doaj.org/toc/1511-788X Journal toc kostenfrei https://doaj.org/toc/2289-7860 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2023 1
allfieldsSound	10.31436/iiumej.v24i1.2380 doi (DE-627)DOAJ08288935X (DE-599)DOAJ297409832f0645688c8c2a174222e0e5 DE-627 ger DE-627 rakwb eng TA1-2040 Kashif Hussain verfasserin aut Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan. Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor Engineering (General). Civil engineering (General) Oluwaseun Adeyeye verfasserin aut Nazihah Ahmad verfasserin aut In International Islamic University Malaysia Engineering Journal IIUM Press, International Islamic University Malaysia, 2015 24(2023), 1 (DE-627)1010842064 22897860 nnns volume:24 year:2023 number:1 https://doi.org/10.31436/iiumej.v24i1.2380 kostenfrei https://doaj.org/article/297409832f0645688c8c2a174222e0e5 kostenfrei https://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/2380 kostenfrei https://doaj.org/toc/1511-788X Journal toc kostenfrei https://doaj.org/toc/2289-7860 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2023 1
language	English
source	In International Islamic University Malaysia Engineering Journal 24(2023), 1 volume:24 year:2023 number:1
sourceStr	In International Islamic University Malaysia Engineering Journal 24(2023), 1 volume:24 year:2023 number:1
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor Engineering (General). Civil engineering (General)
isfreeaccess_bool	true
container_title	International Islamic University Malaysia Engineering Journal
authorswithroles_txt_mv	Kashif Hussain @@aut@@ Oluwaseun Adeyeye @@aut@@ Nazihah Ahmad @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	1010842064
id	DOAJ08288935X
language_de	englisch
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Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. 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author	Kashif Hussain
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topic_title	TA1-2040 Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems Fuzzy Initial Value Problem First-Order Generalised Steplength Block Method Higher Derivative Charging and Discharging of Capacitor
topic	misc TA1-2040 misc Fuzzy Initial Value Problem misc First-Order misc Generalised Steplength misc Block Method misc Higher Derivative misc Charging and Discharging of Capacitor misc Engineering (General). Civil engineering (General)
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title	Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems
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title_sort	higher derivative block method with generalised steplength for solving first-order fuzzy initial value problems
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title_auth	Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems
abstract	Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan.
abstractGer	Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan.
abstract_unstemmed	Block methods have been adopted in studies for solving first and higher order differential equations due to its impressive accuracy property. Taking a step further to improve this accuracy, researchers have considered the inclusion of higher-derivative terms in the block method, although this has been limited to the presence of one higher-derivative term in previous studies. Hence, this article aims at better accuracy by introducing two higher-derivative terms in the block method. In addition, this article presents a scheme with generalised step length such that there is flexibility on the choice of step length when developing the block method. The generalised step length scheme is adopted to develop a three-step block method for solving first-order fuzzy initial value problems. Its properties to ensure convergence and to show the region of absolute stability is investigated, and problems relating to charging and discharging of capacitor are considered. The absolute error shows the impressive accuracy of the three-step block method including obtaining the same values as the exact solution. Therefore, in addition to the new generalised algorithm presented in this article, a new three-step method for solving linear and nonlinear first order fuzzy initial value problems is presented. ABSTRAK: Kaedah blok digunakan dalam banyak kajian untuk menyelesaikan persamaan pembezaan peringkat pertama dan peringkat tinggi kerana sifat ketepatannya yang baik. Bagi meningkatkan ketepatan ini, penyelidik telah mengambil kira dengan memasukkan terbitan peringkat tinggi dalam kaedah blok, walaupun ini terhad pada satu sebutan terbitan peringkat tinggi dalam kajian sebelum. Oleh itu, kajian ini bertujuan bagi mendapatkan ketepatan yang lebih baik dengan memperkenalkan dua sebutan terbitan peringkat tinggi dalam kaedah blok. Tambahan, kajian ini memperkenalkan skema dengan panjang-langkah kaki biasa supaya terdapat kebolehlenturan pada pilihan langkah semasa membangunkan kaedah blok. Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan.
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title_short	Higher Derivative Block Method with Generalised Steplength for Solving First-Order Fuzzy Initial Value Problems
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Skema ini diadaptasi bagi membangunkan kaedah blok tiga-langkah bagi menyelesai masalah nilai awal peringkat pertama secara rawak. Ciri-ciri terperinci dikaji bagi memastikan penumpuan lingkungan kestabilan mutlak, dan masalah berkaitan pengecasan dan nyahcas kapasitor juga turut diambil kira. Ralat mutlak menunjukkan ketepatan yang mengkagumkan pada kaedah blok tiga-langkah termasuk mendapatkan nilai yang sama seperti penyelesaian. Oleh itu, tambahan pada algoritma ini, kaedah tiga-langkah bagi menyelesaikan linear dan tidak linear pada masalah nilai awal peringat pertama secara rawak diperkenalkan.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fuzzy Initial Value Problem</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">First-Order</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Generalised Steplength</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Block Method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Higher Derivative</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Charging and Discharging of Capacitor</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Engineering (General). 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