On the numerical solution of high order multi-dimensional elliptic PDEs

Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used....
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ghasemi, M. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds

Übergeordnetes Werk:	Enthalten in: Computers and mathematics with applications - Amsterdam [u.a.] : Elsevier Science, 1975, 76, Seite 1228-1245
Übergeordnetes Werk:	volume:76 ; pages:1228-1245

DOI / URN:	10.1016/j.camwa.2018.06.017

Katalog-ID:	ELV000316857

Internformat


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024	7		\|a 10.1016/j.camwa.2018.06.017 \|2 doi
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100	1		\|a Ghasemi, M. \|e verfasserin \|0 (orcid)0000-0003-0068-0707 \|4 aut
245	1	0	\|a On the numerical solution of high order multi-dimensional elliptic PDEs
264		1	\|c 2018
336			\|a nicht spezifiziert \|b zzz \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms.
650		4	\|a Differential quadrature method
650		4	\|a Elliptic PDEs
650		4	\|a Biharmonic equation
650		4	\|a Triharmonic equation
650		4	\|a Error bounds
773	0	8	\|i Enthalten in \|t Computers and mathematics with applications \|d Amsterdam [u.a.] : Elsevier Science, 1975 \|g 76, Seite 1228-1245 \|h Online-Ressource \|w (DE-627)320435121 \|w (DE-600)2004251-6 \|w (DE-576)259271225 \|x 1873-7668 \|7 nnns
773	1	8	\|g volume:76 \|g pages:1228-1245
912			\|a GBV_USEFLAG_U
912			\|a SYSFLAG_U
912			\|a GBV_ELV
912			\|a SSG-OPC-MAT
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_647
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.80 \|j Angewandte Mathematik
936	b	k	\|a 54.80 \|j Angewandte Informatik
951			\|a AR
952			\|d 76 \|h 1228-1245

Indexfelder

author_variant	m g mg
matchkey_str	article:18737668:2018----::nhnmrclouinfihremliies
hierarchy_sort_str	2018
bklnumber	31.80 54.80
publishDate	2018
allfields	10.1016/j.camwa.2018.06.017 doi (DE-627)ELV000316857 (ELSEVIER)S0898-1221(18)30341-9 DE-627 ger DE-627 rda eng 510 004 DE-600 31.80 bkl 54.80 bkl Ghasemi, M. verfasserin (orcid)0000-0003-0068-0707 aut On the numerical solution of high order multi-dimensional elliptic PDEs 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms. Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 76, Seite 1228-1245 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:76 pages:1228-1245 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik 54.80 Angewandte Informatik AR 76 1228-1245
spelling	10.1016/j.camwa.2018.06.017 doi (DE-627)ELV000316857 (ELSEVIER)S0898-1221(18)30341-9 DE-627 ger DE-627 rda eng 510 004 DE-600 31.80 bkl 54.80 bkl Ghasemi, M. verfasserin (orcid)0000-0003-0068-0707 aut On the numerical solution of high order multi-dimensional elliptic PDEs 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms. Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 76, Seite 1228-1245 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:76 pages:1228-1245 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik 54.80 Angewandte Informatik AR 76 1228-1245
allfields_unstemmed	10.1016/j.camwa.2018.06.017 doi (DE-627)ELV000316857 (ELSEVIER)S0898-1221(18)30341-9 DE-627 ger DE-627 rda eng 510 004 DE-600 31.80 bkl 54.80 bkl Ghasemi, M. verfasserin (orcid)0000-0003-0068-0707 aut On the numerical solution of high order multi-dimensional elliptic PDEs 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms. Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 76, Seite 1228-1245 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:76 pages:1228-1245 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik 54.80 Angewandte Informatik AR 76 1228-1245
allfieldsGer	10.1016/j.camwa.2018.06.017 doi (DE-627)ELV000316857 (ELSEVIER)S0898-1221(18)30341-9 DE-627 ger DE-627 rda eng 510 004 DE-600 31.80 bkl 54.80 bkl Ghasemi, M. verfasserin (orcid)0000-0003-0068-0707 aut On the numerical solution of high order multi-dimensional elliptic PDEs 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms. Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 76, Seite 1228-1245 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:76 pages:1228-1245 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik 54.80 Angewandte Informatik AR 76 1228-1245
allfieldsSound	10.1016/j.camwa.2018.06.017 doi (DE-627)ELV000316857 (ELSEVIER)S0898-1221(18)30341-9 DE-627 ger DE-627 rda eng 510 004 DE-600 31.80 bkl 54.80 bkl Ghasemi, M. verfasserin (orcid)0000-0003-0068-0707 aut On the numerical solution of high order multi-dimensional elliptic PDEs 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms. Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 76, Seite 1228-1245 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:76 pages:1228-1245 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik 54.80 Angewandte Informatik AR 76 1228-1245
language	English
source	Enthalten in Computers and mathematics with applications 76, Seite 1228-1245 volume:76 pages:1228-1245
sourceStr	Enthalten in Computers and mathematics with applications 76, Seite 1228-1245 volume:76 pages:1228-1245
format_phy_str_mv	Article
bklname	Angewandte Mathematik Angewandte Informatik
institution	findex.gbv.de
topic_facet	Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds
dewey-raw	510
isfreeaccess_bool	false
container_title	Computers and mathematics with applications
authorswithroles_txt_mv	Ghasemi, M. @@aut@@
publishDateDaySort_date	2018-01-01T00:00:00Z
hierarchy_top_id	320435121
dewey-sort	3510
id	ELV000316857
language_de	englisch
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author	Ghasemi, M.
spellingShingle	Ghasemi, M. ddc 510 bkl 31.80 bkl 54.80 misc Differential quadrature method misc Elliptic PDEs misc Biharmonic equation misc Triharmonic equation misc Error bounds On the numerical solution of high order multi-dimensional elliptic PDEs
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topic_title	510 004 DE-600 31.80 bkl 54.80 bkl On the numerical solution of high order multi-dimensional elliptic PDEs Differential quadrature method Elliptic PDEs Biharmonic equation Triharmonic equation Error bounds
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title	On the numerical solution of high order multi-dimensional elliptic PDEs
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title_full	On the numerical solution of high order multi-dimensional elliptic PDEs
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title_sort	on the numerical solution of high order multi-dimensional elliptic pdes
title_auth	On the numerical solution of high order multi-dimensional elliptic PDEs
abstract	Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms.
abstractGer	Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms.
abstract_unstemmed	Using the idea of differential quadrature, two new methods are constructed to approximate the solution of elliptic partial differential equations in higher dimensions. To obtain the weighting coefficients of the first method, a mixture of grid points and mid points of the uniform partition is used. The order of convergence obtained by the first algorithm is non-optimal, so we mixed the idea with spline collocation to obtain higher order approximations. Using the weighting coefficients of the non-optimal algorithm, some new weighting coefficients are obtained which are used to obtain higher accuracy. For the first time, a sixth order approximation is obtained to the solution of well-known high order multi-dimensional elliptic PDEs such as biharmonic and triharmonic problems. We found a way to increase the order of convergence and the accuracy without increasing the CPU runtime. The block form of the coefficients matrix for the linear case is presented to have a better vision on the system arised from the method. Some examples of biharmonic and triharmonic problems are solved to show the good performance and applicability of the proposed algorithms.
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title_short	On the numerical solution of high order multi-dimensional elliptic PDEs
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On the numerical solution of high order multi-dimensional elliptic PDEs

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