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Solving the Fokker-Planck equation via the compact finite difference method | ||
| Computational Methods for Differential Equations | ||
| مقاله 7، دوره 8، شماره 3، آبان 2020، صفحه 493-504 اصل مقاله (133.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.28609.1396 | ||
| نویسندگان | ||
| Behnam Sepehrian* 1؛ Marzieh Karimi Radpoor2 | ||
| 1Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran. | ||
| 2Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran. | ||
| چکیده | ||
| In this study, we solve the Fokker-Planck equation by a compact finite difference method. By the finite difference method the computation of Fokker-Planck equation is reduced to a system of ordinary differential equations. Two different methods, boundary value method and cubic $C^1$-spline collocation method, for solving the resulting system are proposed. Both methods have fourth order accuracy in time variable. By the boundary value method some pointwise approximate solutions are only obtained. But, $C^1$-spline method gives a closed form approximation in each space step, too. Illustrative examples are included to demonstrate the validity and efficiency of the methods. A comparison is made with existing results. | ||
| کلیدواژهها | ||
| Boundary value method؛ Collocation method؛ Compact method؛ Cubic C$^1$-spline؛ Fokker-Planck equation | ||
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آمار تعداد مشاهده مقاله: 410 تعداد دریافت فایل اصل مقاله: 315 |
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