Second order balanced stochastic runge kutta methods with split drift and algebraic equations

Abstract

In recent times stochastic modelling and numerical solutions to newlinestochastic differential equations are developing at much faster pace Stochastic differential equations have a wide applications in the field of biological modelling signal transmissions financial mathematics and epidemiology But the study of simulations due to electric circuits cannot be handled by stochastic differential equations The electric circuit simulations and mechanics of the systems can be studied by using stochastic differential algebraic equations Two classes of balanced stochastic Runge Kutta methods are constructed for multi-dimensional It o stochastic differential systems The balanced methods are used in order to obtain better stability than the stochastic Runge Kutta methods By the optimal choice of the parameters of the control functions the numerical mean square stability analysis and the strong convergent properties of secondorder balanced stochastic Runge Kutta numerical methods for k stages are obtained The preservation of the sign of the initial data is obtained for balanced stochastic Runge Kutta methods The splitting technique for the two classes of weak second-order balanced stochastic Runge Kutta methods are analyzed to improve the stability properties of the method newline newline