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A boundary element method for fractional diffusion-reaction equations | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 07 شهریور 1405 اصل مقاله (1.88 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.32630.2966 | ||
| نویسندگان | ||
| Leila Hasani1؛ AllahBakhsh Yazdani Cherati* 2؛ Afshin Babaei1 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. | ||
| چکیده | ||
| In this study, a boundary element method based on the Caputo derivative is developed for solving the time-fractional diffusion–reaction equation. The model describes anomalous transport behavior coupled with a linear reaction term. The numerical algorithm is implemented in MATLAB, providing an efficient computational framework for fractional analysis. Numerical results for a two-dimensional strip domain show very good agreement with the analytical solution, with a maximum relative error below 0.2%. The method demonstrates stable and accurate behavior for reaction parameters in the range 0 ≤ λ ≲ 0.1, where both boundary and interior errors remain small. For larger reaction parameters, the internal numerical errors increase due to the stronger stiffness introduced by the reaction term. The observed temporal convergence is consistent with the expected behavior of fractional diffusion equations on uniform time grids. | ||
| کلیدواژهها | ||
| Fractional diffusion؛ Caputo derivative؛ boundary element method؛ diffusion-reaction | ||
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