STOCHASTIC RUNGE-KUTTA ROSENBROCK TYPE SCHEME WITH STRONG GLOBAL ORDER ONE FOR STOCHASTIC DIFFERENTIAL EQUATIONS

The analytical investigations and numerical solutions of stochastic differen tial equations have always been of interest to researchers. During the several decades, many efficient methods have been developed for solving different types of stochastic dif ferential equations with different properties. We need numerical methods because a lot of stochastic differential equations are not analytically solvable. There are two dominating versions of stochastic calculus, the Itô stochastic calculus and the Stratonovich stochastic calculus. In this work, we concern the new class of stochastic Runge-Kutta method for solution of Stratonovich stochastic differential equations with scalar noise. Using Rosen brock ordinary differential equation solver, we define stochastic Runge-Kutta Rosenbrock type scheme. In recent years, implicit stochastic Runge?Kutta methods have been devel oped both for strong and weak approximations. For these methods, the stage values are only given implicitly. Stratonovich Taylor expansion is applied to derive strong global convergence order 1.0. Also, mean-square stability is studied and some examples are presented to support the theoretical results.