A new spectral method using Mittag-Leffler wavelets for solving stochastic differential equations

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 23 October 2025

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History

  • Receive Date: 17 March 2025
  • Revise Date: 15 October 2025
  • Accept Date: 19 October 2025

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