The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation
The paper proposes a method to solve the time fractional Fokker–Planck equation using the generalized Hermite spectral method and Laplace transform. By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2024/1071446 |
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| _version_ | 1832559284045479936 |
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| author | Lu-feng Yang |
| author_facet | Lu-feng Yang |
| author_sort | Lu-feng Yang |
| collection | DOAJ |
| description | The paper proposes a method to solve the time fractional Fokker–Planck equation using the generalized Hermite spectral method and Laplace transform. By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. The orthogonal expansion coefficients of frequency domain components are obtained through this transformation. The approximate solution at any time is then obtained by using the numerical inverse Laplace transform with the Talbot algorithm. Numerical experiments have been carried out to demonstrate the high accuracy and efficiency of the proposed method. |
| format | Article |
| id | doaj-art-6d5a09d60c3741bcacaf1fd386e04ffc |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-6d5a09d60c3741bcacaf1fd386e04ffc2025-02-03T01:30:21ZengWileyAdvances in Mathematical Physics1687-91392024-01-01202410.1155/2024/1071446The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck EquationLu-feng Yang0School of Mathematics and Information ScienceThe paper proposes a method to solve the time fractional Fokker–Planck equation using the generalized Hermite spectral method and Laplace transform. By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. The orthogonal expansion coefficients of frequency domain components are obtained through this transformation. The approximate solution at any time is then obtained by using the numerical inverse Laplace transform with the Talbot algorithm. Numerical experiments have been carried out to demonstrate the high accuracy and efficiency of the proposed method.http://dx.doi.org/10.1155/2024/1071446 |
| spellingShingle | Lu-feng Yang The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation Advances in Mathematical Physics |
| title | The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation |
| title_full | The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation |
| title_fullStr | The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation |
| title_full_unstemmed | The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation |
| title_short | The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation |
| title_sort | generalized hermite spectral method combined with laplace transform for solution of the time fractional fokker planck equation |
| url | http://dx.doi.org/10.1155/2024/1071446 |
| work_keys_str_mv | AT lufengyang thegeneralizedhermitespectralmethodcombinedwithlaplacetransformforsolutionofthetimefractionalfokkerplanckequation AT lufengyang generalizedhermitespectralmethodcombinedwithlaplacetransformforsolutionofthetimefractionalfokkerplanckequation |