Applying Legendre wavelet method with Tikhonov regularization for one-dimensional time-fractional diffusion equations
| Autor: | J. Saeidian, Aram Azizi, Sarkout Abdi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Legendre wavelet
Applied Mathematics 010103 numerical & computational mathematics 01 natural sciences Regularization (mathematics) 010101 applied mathematics Tikhonov regularization Computational Mathematics Algebraic equation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Fractional diffusion Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Computational and Applied Mathematics. 37:4793-4804 |
| ISSN: | 1807-0302 0101-8205 |
| DOI: | 10.1007/s40314-018-0593-7 |
| Popis: | In this paper, a new method based on two-dimensional Legendre wavelet basis is proposed to solve time-fractional diffusion equations. This technique is used to convert the problem into a system of linear algebraic equations via expanding the required approximation based on the Legendre wavelet basis. The effectiveness of the proposed method is examined by comparing the numerical results with other methods. When the desired system is large, it is ill-conditioned; in this case, Tikhonov regularization method, with discrepancy principle for finding the regularization parameter, is applied to stabilize the solution. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink