Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method
In this paper, we present a Crank-Nicolson collocation method based on modified Quintic B-splines for parabolic PDEs. The time-dependent convection–diffusion equation (CDE) and Burgers’ equation are considered. The integration of the problem is handled by using a modified quintic B-spline, over Cran...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-06-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447920302367 |
| _version_ | 1818437492753301504 |
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| author | Mohammad Tamsir Neeraj Dhiman Amit Chauhan Anand Chauhan |
| author_facet | Mohammad Tamsir Neeraj Dhiman Amit Chauhan Anand Chauhan |
| author_sort | Mohammad Tamsir |
| collection | DOAJ |
| description | In this paper, we present a Crank-Nicolson collocation method based on modified Quintic B-splines for parabolic PDEs. The time-dependent convection–diffusion equation (CDE) and Burgers’ equation are considered. The integration of the problem is handled by using a modified quintic B-spline, over Crank-Nicolson (C-N) scheme, in space. The time-dependent terms are discretized using FDM. The efficiency as well as the accuracy of the method checked through the six numerical examples. The approximate results are presented and compared with the known exact and other numerical solutions. The Von Neumann stability is also performed. |
| first_indexed | 2024-12-14T17:25:32Z |
| format | Article |
| id | doaj.art-34e26acf84bc47c1a4795756d6289a9a |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-14T17:25:32Z |
| publishDate | 2021-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-34e26acf84bc47c1a4795756d6289a9a2022-12-21T22:53:13ZengElsevierAin Shams Engineering Journal2090-44792021-06-0112220732082Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation methodMohammad Tamsir0Neeraj Dhiman1Amit Chauhan2Anand Chauhan3Department of Mathematics, Jazan University, Jazan, Saudi ArabiaDepartment of Mathematics, Graphic Era Hill University, Dehradun 248002, India; Corresponding author.Department of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, India; Departmet of Mathematics D.B.S. (P.G.) College, Dehradun 248002, IndiaDepartment of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, IndiaIn this paper, we present a Crank-Nicolson collocation method based on modified Quintic B-splines for parabolic PDEs. The time-dependent convection–diffusion equation (CDE) and Burgers’ equation are considered. The integration of the problem is handled by using a modified quintic B-spline, over Crank-Nicolson (C-N) scheme, in space. The time-dependent terms are discretized using FDM. The efficiency as well as the accuracy of the method checked through the six numerical examples. The approximate results are presented and compared with the known exact and other numerical solutions. The Von Neumann stability is also performed.http://www.sciencedirect.com/science/article/pii/S2090447920302367Quintic B-spline basis functionsConvection-diffusion equationBurgers’ equationC-N schemeGauss elimination methodStability |
| spellingShingle | Mohammad Tamsir Neeraj Dhiman Amit Chauhan Anand Chauhan Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method Ain Shams Engineering Journal Quintic B-spline basis functions Convection-diffusion equation Burgers’ equation C-N scheme Gauss elimination method Stability |
| title | Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method |
| title_full | Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method |
| title_fullStr | Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method |
| title_full_unstemmed | Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method |
| title_short | Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method |
| title_sort | solution of parabolic pdes by modified quintic b spline crank nicolson collocation method |
| topic | Quintic B-spline basis functions Convection-diffusion equation Burgers’ equation C-N scheme Gauss elimination method Stability |
| url | http://www.sciencedirect.com/science/article/pii/S2090447920302367 |
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