Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets
A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/964623 |
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| _version_ | 1832553729653473280 |
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| author | Xiaoyong Xu Fengying Zhou |
| author_facet | Xiaoyong Xu Fengying Zhou |
| author_sort | Xiaoyong Xu |
| collection | DOAJ |
| description | A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. The uniform convergence analysis and error estimation for the proposed method are given. Accuracy and efficiency of the suggested method are established through comparing with the existing quintic B-spline collocation method, homotopy asymptotic method, and modified decomposition method. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literatures. |
| format | Article |
| id | doaj-art-1da4cbe4e3b345be83c9e4907b0835e8 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-1da4cbe4e3b345be83c9e4907b0835e82025-02-03T05:53:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/964623964623Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev WaveletsXiaoyong Xu0Fengying Zhou1School of Science, East China Institute of Technology, Nanchang 330013, ChinaSchool of Science, East China Institute of Technology, Nanchang 330013, ChinaA collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. The uniform convergence analysis and error estimation for the proposed method are given. Accuracy and efficiency of the suggested method are established through comparing with the existing quintic B-spline collocation method, homotopy asymptotic method, and modified decomposition method. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literatures.http://dx.doi.org/10.1155/2015/964623 |
| spellingShingle | Xiaoyong Xu Fengying Zhou Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets Advances in Mathematical Physics |
| title | Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets |
| title_full | Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets |
| title_fullStr | Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets |
| title_full_unstemmed | Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets |
| title_short | Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets |
| title_sort | numerical solutions for the eighth order initial and boundary value problems using the second kind chebyshev wavelets |
| url | http://dx.doi.org/10.1155/2015/964623 |
| work_keys_str_mv | AT xiaoyongxu numericalsolutionsfortheeighthorderinitialandboundaryvalueproblemsusingthesecondkindchebyshevwavelets AT fengyingzhou numericalsolutionsfortheeighthorderinitialandboundaryvalueproblemsusingthesecondkindchebyshevwavelets |