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Fourth-order numerical method for the Riesz space fractional diffusion equation with a nonlinear source term | ||
| Computational Methods for Differential Equations | ||
| مقاله 7، دوره 9، شماره 3، مهر 2021، صفحه 736-748 اصل مقاله (150.59 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.36930.1643 | ||
| نویسنده | ||
| Akbar Mohebbi* | ||
| Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran. | ||
| چکیده | ||
| This paper aims to propose a high-order and accurate numerical scheme for the solution of the nonlinear diffusion equation with Riesz space fractional derivative. To this end, we first discretize the Riesz fractional derivative with a fourth-order finite difference method, then we apply a boundary value method (BVM) of fourth-order for the time integration of the resulting system of ordinary differential equations. The proposed method has a fourth-order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of BVM. The numerical results are compared with analytical solutions and with those provided by other methods in the literature. Numerical experiments obtained from solving several problems including fractional Fisher and fractional parabolic-type sine-Gordon equations show that the proposed method is an efficient algorithm for solving such problems and can arrive at the high-precision. | ||
| کلیدواژهها | ||
| Compact finite difference method؛ Boundary value methods؛ Riesz space fractional derivatives؛ Unconditional stability؛ Diffusion equation | ||
| مراجع | ||
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