Modified Chebyshev Collocation Method for Solving Differential Equations
This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial) collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial) collocation method is applied to both Ordinary Diffe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2015-05-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| Subjects: | |
| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/2923 |
| _version_ | 1818200570857521152 |
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| author | M Ziaul Arif Ahmad Kamsyakawuni Ikhsanul Halikin |
| author_facet | M Ziaul Arif Ahmad Kamsyakawuni Ikhsanul Halikin |
| author_sort | M Ziaul Arif |
| collection | DOAJ |
| description | This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial) collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial) collocation method is applied to both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given. |
| first_indexed | 2024-12-12T02:39:46Z |
| format | Article |
| id | doaj.art-47756b0523d04824b643fbec46429fe9 |
| institution | Directory Open Access Journal |
| issn | 2086-0382 2477-3344 |
| language | English |
| last_indexed | 2024-12-12T02:39:46Z |
| publishDate | 2015-05-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj.art-47756b0523d04824b643fbec46429fe92022-12-22T00:41:12ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442015-05-013420821310.18860/ca.v3i4.29232607Modified Chebyshev Collocation Method for Solving Differential EquationsM Ziaul Arif0Ahmad Kamsyakawuni1Ikhsanul Halikin2Department of Mathematics, Faculty of Sciences, University of JemberDepartment of Mathematics, Faculty of Sciences, University of JemberDepartment of Mathematics, Faculty of Sciences, University of JemberThis paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial) collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial) collocation method is applied to both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/2923vieta-lucas polynomialcollocation methodordinary differential equationspartial differential equationsfinite difference methods |
| spellingShingle | M Ziaul Arif Ahmad Kamsyakawuni Ikhsanul Halikin Modified Chebyshev Collocation Method for Solving Differential Equations Cauchy: Jurnal Matematika Murni dan Aplikasi vieta-lucas polynomial collocation method ordinary differential equations partial differential equations finite difference methods |
| title | Modified Chebyshev Collocation Method for Solving Differential Equations |
| title_full | Modified Chebyshev Collocation Method for Solving Differential Equations |
| title_fullStr | Modified Chebyshev Collocation Method for Solving Differential Equations |
| title_full_unstemmed | Modified Chebyshev Collocation Method for Solving Differential Equations |
| title_short | Modified Chebyshev Collocation Method for Solving Differential Equations |
| title_sort | modified chebyshev collocation method for solving differential equations |
| topic | vieta-lucas polynomial collocation method ordinary differential equations partial differential equations finite difference methods |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/2923 |
| work_keys_str_mv | AT mziaularif modifiedchebyshevcollocationmethodforsolvingdifferentialequations AT ahmadkamsyakawuni modifiedchebyshevcollocationmethodforsolvingdifferentialequations AT ikhsanulhalikin modifiedchebyshevcollocationmethodforsolvingdifferentialequations |