Numerical Accuracy of Euler-Maruyama and Milstein Methods for Solving Nonlinear Stochastic Differential Equation

Abstract

In this paper we examine the numerical accuracy of two widely used methods-the Euler–Maruyama and Milstein methods for solving Stochastic Differential Equations (SDEs). In this study we deal with two nonlinear SDEs, whose exact solutions are derived using Itô’s calculus. Using uniform discretization conditions, the comparative study is made on the exact solutions, approximate solutions, and absolute errors, supported with graphs and tables. This study focuses on selecting reliable numerical methods for accurately solving nonlinear stochastic systems.