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A new spectral method using Mittag-Leffler wavelets for solving stochastic differential equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 آبان 1404 اصل مقاله (1.21 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66447.3101 | ||
| نویسندگان | ||
| Fateme Yari؛ Farshid Mirzaee* ؛ Erfan Solhi | ||
| Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran. | ||
| چکیده | ||
| This paper introduces a novel numerical method for solving stochastic differential equations using a newly developed basis of Mittag-Leffler wavelets. The proposed approach integrates the collocation and numerical integration methods to approximate solutions, effectively transforming the problem into a nonlinear system of equations that is efficiently solved using the Newton method. The Mittag-Leffler wavelets significantly enhance the effectiveness of the numerical approximations. Numerical experiments, including comparisons with other existing methods, demonstrate the superior accuracy and computational efficiency of the proposed method, especially for nonlinear problems influenced by stochastic noise. The simplicity and robustness of this method make it a powerful tool for solving stochastic problems. These findings underscore the potential of the proposed technique to advance the numerical solution of stochastic differential equations. | ||
| کلیدواژه‌ها | ||
| Mittag-Leffler wavelets؛ Stochastic differential equations؛ Collocation method, Numerical integration | ||
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آمار تعداد مشاهده مقاله: 45 تعداد دریافت فایل اصل مقاله: 68 |
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