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A method of lines for solving the nonlinear time- and space-fractional Schrodinger equation via stable Gaussian radial basis function interpolation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 اردیبهشت 1403 اصل مقاله (758.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.54090.2265 | ||
| نویسندگان | ||
| Behnam Sepehrian* ؛ Zahra Shamohammadi | ||
| Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran. | ||
| چکیده | ||
| The stable Gaussian radial basis function (RBF) interpolation is applied to solve the time- and space-fractional Schrodinger equation (TSFSE) in one and two dimensional cases. In this regard, the fractional derivatives of stable Gaussian radial basis function interpolants are obtained. By a method of lines the computations of the TSFSE are converted to a coupled system of Caputo fractional ODEs. To solve the resulted system of ODEs, a high order finite difference method is proposed, and the computations are reduced to a coupled system of nonlinear algebraic equations, in each time step. Numerical illustrations are performed to certify the ability and accuracy of the new method. Some comparisons are made with the results in other literature. | ||
| کلیدواژه‌ها | ||
| Caputo derivative؛ Nonlinear؛ Fractional Schrodinger equation؛ Radial basis functions؛ Riesz derivative | ||
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آمار تعداد مشاهده مقاله: 12 تعداد دریافت فایل اصل مقاله: 47 |
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