stochastic runge-kutta rosenbrock type scheme with strong global order one for stochastic differential equations

The analytical investigations and numerical solutions of stochastic differential equations have always been of interest to researchers. during the several decades,many efficient methods have been developed for solving different types of stochastic differential equations with different properties. we need numerical methods because a lot ofstochastic differential equations are not analytically solvable. there are two dominatingversions of stochastic calculus, the itô stochastic calculus and the stratonovich stochasticcalculus. in this work, we concern the new class of stochastic runge-kutta method forsolution of stratonovich stochastic differential equations with scalar noise. using rosenbrock ordinary differential equation solver, we define stochastic runge-kutta rosenbrocktype scheme. in recent years, implicit stochastic runge?kutta methods have been developed both for strong and weak approximations. for these methods, the stage values areonly given implicitly. stratonovich taylor expansion is applied to derive strong globalconvergence order 1.0. also, mean-square stability is studied and some examples arepresented to support the theoretical results.