Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions |
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Authors: | MH Heydari MR Hooshmandasl FM Maalek Ghaini F Fereidouni |
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Affiliation: | 1. Faculty of Mathematics, Yazd University, Yazd, Iran;2. Faculty of Mining Engineering, Yazd University, Yazd, Iran |
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Abstract: | In this paper, the two-dimensional Legendre wavelets are applied for numerical solution of the fractional Poisson equation with Dirichlet boundary conditions. In this way, a new operational matrix of fractional derivative for the Legendre wavelets is derived and then this operational matrix has been employed to obtain the numerical solution of the above-mentioned problem. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problem. The convergence of the two-dimensional Legendre wavelets expansion is investigated. Also the power of this manageable method is illustrated. |
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Keywords: | Legendre wavelets Poisson equation Dirichlet boundary condition Fractional derivative |
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