High-order compact difference methods for solving two-dimensional nonlinear wave equations

Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a n...
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Autor*in:	Shuaikang Wang [verfasserIn] Yunzhi Jiang [verfasserIn] Yongbin Ge [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations

Übergeordnetes Werk:	In: Electronic Research Archive - AIMS Press, 2022, 31(2023), 6, Seite 3145-3168
Übergeordnetes Werk:	volume:31 ; year:2023 ; number:6 ; pages:3145-3168

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3934/era.2023159

Katalog-ID:	DOAJ090001893

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allfields	10.3934/era.2023159 doi (DE-627)DOAJ090001893 (DE-599)DOAJfe10b5a6dad044fb8c9ca8a7886bcad7 DE-627 ger DE-627 rakwb eng QA1-939 T57-57.97 Shuaikang Wang verfasserin aut High-order compact difference methods for solving two-dimensional nonlinear wave equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes. nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations Mathematics Applied mathematics. Quantitative methods Yunzhi Jiang verfasserin aut Yongbin Ge verfasserin aut In Electronic Research Archive AIMS Press, 2022 31(2023), 6, Seite 3145-3168 (DE-627)1835128319 26881594 nnns volume:31 year:2023 number:6 pages:3145-3168 https://doi.org/10.3934/era.2023159 kostenfrei https://doaj.org/article/fe10b5a6dad044fb8c9ca8a7886bcad7 kostenfrei https://www.aimspress.com/article/doi/10.3934/era.2023159?viewType=HTML kostenfrei https://doaj.org/toc/2688-1594 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 31 2023 6 3145-3168
spelling	10.3934/era.2023159 doi (DE-627)DOAJ090001893 (DE-599)DOAJfe10b5a6dad044fb8c9ca8a7886bcad7 DE-627 ger DE-627 rakwb eng QA1-939 T57-57.97 Shuaikang Wang verfasserin aut High-order compact difference methods for solving two-dimensional nonlinear wave equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes. nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations Mathematics Applied mathematics. Quantitative methods Yunzhi Jiang verfasserin aut Yongbin Ge verfasserin aut In Electronic Research Archive AIMS Press, 2022 31(2023), 6, Seite 3145-3168 (DE-627)1835128319 26881594 nnns volume:31 year:2023 number:6 pages:3145-3168 https://doi.org/10.3934/era.2023159 kostenfrei https://doaj.org/article/fe10b5a6dad044fb8c9ca8a7886bcad7 kostenfrei https://www.aimspress.com/article/doi/10.3934/era.2023159?viewType=HTML kostenfrei https://doaj.org/toc/2688-1594 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 31 2023 6 3145-3168
allfields_unstemmed	10.3934/era.2023159 doi (DE-627)DOAJ090001893 (DE-599)DOAJfe10b5a6dad044fb8c9ca8a7886bcad7 DE-627 ger DE-627 rakwb eng QA1-939 T57-57.97 Shuaikang Wang verfasserin aut High-order compact difference methods for solving two-dimensional nonlinear wave equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes. nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations Mathematics Applied mathematics. Quantitative methods Yunzhi Jiang verfasserin aut Yongbin Ge verfasserin aut In Electronic Research Archive AIMS Press, 2022 31(2023), 6, Seite 3145-3168 (DE-627)1835128319 26881594 nnns volume:31 year:2023 number:6 pages:3145-3168 https://doi.org/10.3934/era.2023159 kostenfrei https://doaj.org/article/fe10b5a6dad044fb8c9ca8a7886bcad7 kostenfrei https://www.aimspress.com/article/doi/10.3934/era.2023159?viewType=HTML kostenfrei https://doaj.org/toc/2688-1594 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 31 2023 6 3145-3168
allfieldsGer	10.3934/era.2023159 doi (DE-627)DOAJ090001893 (DE-599)DOAJfe10b5a6dad044fb8c9ca8a7886bcad7 DE-627 ger DE-627 rakwb eng QA1-939 T57-57.97 Shuaikang Wang verfasserin aut High-order compact difference methods for solving two-dimensional nonlinear wave equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes. nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations Mathematics Applied mathematics. Quantitative methods Yunzhi Jiang verfasserin aut Yongbin Ge verfasserin aut In Electronic Research Archive AIMS Press, 2022 31(2023), 6, Seite 3145-3168 (DE-627)1835128319 26881594 nnns volume:31 year:2023 number:6 pages:3145-3168 https://doi.org/10.3934/era.2023159 kostenfrei https://doaj.org/article/fe10b5a6dad044fb8c9ca8a7886bcad7 kostenfrei https://www.aimspress.com/article/doi/10.3934/era.2023159?viewType=HTML kostenfrei https://doaj.org/toc/2688-1594 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 31 2023 6 3145-3168
allfieldsSound	10.3934/era.2023159 doi (DE-627)DOAJ090001893 (DE-599)DOAJfe10b5a6dad044fb8c9ca8a7886bcad7 DE-627 ger DE-627 rakwb eng QA1-939 T57-57.97 Shuaikang Wang verfasserin aut High-order compact difference methods for solving two-dimensional nonlinear wave equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes. nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations Mathematics Applied mathematics. Quantitative methods Yunzhi Jiang verfasserin aut Yongbin Ge verfasserin aut In Electronic Research Archive AIMS Press, 2022 31(2023), 6, Seite 3145-3168 (DE-627)1835128319 26881594 nnns volume:31 year:2023 number:6 pages:3145-3168 https://doi.org/10.3934/era.2023159 kostenfrei https://doaj.org/article/fe10b5a6dad044fb8c9ca8a7886bcad7 kostenfrei https://www.aimspress.com/article/doi/10.3934/era.2023159?viewType=HTML kostenfrei https://doaj.org/toc/2688-1594 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 31 2023 6 3145-3168
language	English
source	In Electronic Research Archive 31(2023), 6, Seite 3145-3168 volume:31 year:2023 number:6 pages:3145-3168
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topic_facet	nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations Mathematics Applied mathematics. Quantitative methods
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callnumber-first	Q - Science
author	Shuaikang Wang
spellingShingle	Shuaikang Wang misc QA1-939 misc T57-57.97 misc nonlinear wave equation misc nonlinear compact difference scheme misc three-level linearized compact difference scheme misc coupled sine-gordon equations misc Mathematics misc Applied mathematics. Quantitative methods High-order compact difference methods for solving two-dimensional nonlinear wave equations
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topic_title	QA1-939 T57-57.97 High-order compact difference methods for solving two-dimensional nonlinear wave equations nonlinear wave equation nonlinear compact difference scheme three-level linearized compact difference scheme coupled sine-gordon equations
topic	misc QA1-939 misc T57-57.97 misc nonlinear wave equation misc nonlinear compact difference scheme misc three-level linearized compact difference scheme misc coupled sine-gordon equations misc Mathematics misc Applied mathematics. Quantitative methods
topic_unstemmed	misc QA1-939 misc T57-57.97 misc nonlinear wave equation misc nonlinear compact difference scheme misc three-level linearized compact difference scheme misc coupled sine-gordon equations misc Mathematics misc Applied mathematics. Quantitative methods
topic_browse	misc QA1-939 misc T57-57.97 misc nonlinear wave equation misc nonlinear compact difference scheme misc three-level linearized compact difference scheme misc coupled sine-gordon equations misc Mathematics misc Applied mathematics. Quantitative methods
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title	High-order compact difference methods for solving two-dimensional nonlinear wave equations
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title_full	High-order compact difference methods for solving two-dimensional nonlinear wave equations
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title_sort	high-order compact difference methods for solving two-dimensional nonlinear wave equations
callnumber	QA1-939
title_auth	High-order compact difference methods for solving two-dimensional nonlinear wave equations
abstract	Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes.
abstractGer	Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes.
abstract_unstemmed	Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes.
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title_short	High-order compact difference methods for solving two-dimensional nonlinear wave equations
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High-order compact difference methods for solving two-dimensional nonlinear wave equations

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