Modified Runge–Kutta method with convergence analysis for nonlinear stochastic differential equations with Hölder continuous diffusion coefficient

Iranian Journal of Numerical Analysis and Optimization

دوره 13، شماره 2 - شماره پیاپی 25، شهریور 2023، صفحه 285-316   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.78723.1181

نویسنده

A. Haghighi^*

Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.

چکیده

The main goal of this work is to develop and analyze an accurate trun-cated stochastic Runge–Kutta (TSRK2) method to obtain strong numeri-cal solutions of nonlinear one-dimensional stochastic differential equations (SDEs) with continuous Hölder diffusion coefficients. We will establish the strong L1-convergence theory to the TSRK2 method under the local Lipschitz condition plus the one-sided Lipschitz condition for the drift co-efficient and the continuous Hölder condition for the diffusion coefficient at a time T and over a finite time interval [0, T ], respectively. We show that the new method can achieve the optimal convergence order at a finite time T compared to the classical Euler–Maruyama method. Finally, nu-merical examples are given to support the theoretical results and illustrate the validity of the method.

کلیدواژه‌ها

Stochastic differential equation؛ Strong convergence؛ Truncated methods؛ Hölder continuous coefficient

مراجع