We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Modified Runge-Kutta method with convergence analysis for nonlinear stochastic differential equations with Hölder continuous diffusion coefficient.
- Authors
Haghighi, A.
- Abstract
The main goal of this work is to develop and analyze an accurate truncated stochastic Runge-Kutta (TSRK2) method to obtain strong numerical 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 coefficient 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, numerical examples are given to support the theoretical results and illustrate the validity of the method.
- Subjects
RUNGE-Kutta formulas; STOCHASTIC convergence; DIFFUSION coefficients; LIPSCHITZ spaces; NUMERICAL analysis
- Publication
Iranian Journal of Numerical Analysis & Optimization, 2023, Vol 13, Issue 2, p285
- ISSN
2423-6977
- Publication type
Article
- DOI
10.22067/ijnao.2022.78723.1181