Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method
The second-kind Chebyshev wavelets collocation method is applied for solving a class of time-fractional diffusion-wave equation. Fractional integral formula of a single Chebyshev wavelet in the Riemann-Liouville sense is derived by means of shifted Chebyshev polynomials of the second kind. Moreover,...
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/2610804 |
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| author | Fengying Zhou Xiaoyong Xu |
| author_facet | Fengying Zhou Xiaoyong Xu |
| author_sort | Fengying Zhou |
| collection | DOAJ |
| description | The second-kind Chebyshev wavelets collocation method is applied for solving a class of time-fractional diffusion-wave equation. Fractional integral formula of a single Chebyshev wavelet in the Riemann-Liouville sense is derived by means of shifted Chebyshev polynomials of the second kind. Moreover, convergence and accuracy estimation of the second-kind Chebyshev wavelets expansion of two dimensions are given. During the process of establishing the expression of the solution, all the initial and boundary conditions are taken into account automatically, which is very convenient for solving the problem under consideration. Based on the collocation technique, the second-kind Chebyshev wavelets are used to reduce the problem to the solution of a system of linear algebraic equations. Several examples are provided to confirm the reliability and effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-439271b81efc4457aeb640fa0ac1678e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-439271b81efc4457aeb640fa0ac1678e2025-02-03T05:52:36ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/26108042610804Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation MethodFengying Zhou0Xiaoyong Xu1School of Science, East China University of Technology, Nanchang 330013, ChinaSchool of Science, East China University of Technology, Nanchang 330013, ChinaThe second-kind Chebyshev wavelets collocation method is applied for solving a class of time-fractional diffusion-wave equation. Fractional integral formula of a single Chebyshev wavelet in the Riemann-Liouville sense is derived by means of shifted Chebyshev polynomials of the second kind. Moreover, convergence and accuracy estimation of the second-kind Chebyshev wavelets expansion of two dimensions are given. During the process of establishing the expression of the solution, all the initial and boundary conditions are taken into account automatically, which is very convenient for solving the problem under consideration. Based on the collocation technique, the second-kind Chebyshev wavelets are used to reduce the problem to the solution of a system of linear algebraic equations. Several examples are provided to confirm the reliability and effectiveness of the proposed method.http://dx.doi.org/10.1155/2017/2610804 |
| spellingShingle | Fengying Zhou Xiaoyong Xu Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method Advances in Mathematical Physics |
| title | Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method |
| title_full | Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method |
| title_fullStr | Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method |
| title_full_unstemmed | Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method |
| title_short | Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method |
| title_sort | numerical solution of time fractional diffusion wave equations via chebyshev wavelets collocation method |
| url | http://dx.doi.org/10.1155/2017/2610804 |
| work_keys_str_mv | AT fengyingzhou numericalsolutionoftimefractionaldiffusionwaveequationsviachebyshevwaveletscollocationmethod AT xiaoyongxu numericalsolutionoftimefractionaldiffusionwaveequationsviachebyshevwaveletscollocationmethod |