Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations

Abstract

<abstract> <p>In this paper, a numerical method to solve a class of stochastic nonlinear differential equations is introduced. The proposed method is based on the Temimi-Ansari method. The special states of the four systems are studied to show that the proposed method is efficient and applicable. These systems are stochastic Langevin's equation, Ginzburg-Landau equation, Davis-Skodje, and Brusselator systems. The results clarify the accuracy and efficacy of the presented new method with no need for any restrictive assumptions for nonlinear terms.</p> </abstract>

Improvement of Split-Step Forward Milstein Schemes for SODEs Arising in Mathematical Physics

“…Stochastic ordinary di erential equations (SODEs) play a pivotal role in explaining some physical phenomena such as chemical reactions [9], nancial mathematics [10], mathematical ecology [11], epidemiology [12], medicine [13], and population dynamics [14]. Generally, SODEs cannot be solved analytical, but many numerical solutions can be found, for instance, the split-step theta Milstein method [15], the least-squares method [16], the discrete Temimi-Ansari method [17], the improved Euler-Maruyama method [18], the ve-stage Milstein method [19], the split-step Milstein method [20], the split-step Adams-Moulton Milstein method [21], the split-step forward Milstein method [22], and the Runge-Kutta method [23,24].…”