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We consider numerical solutions of stochastic initial value problems via the random Runge-Kutta method of the fourth order. A random mean value theorem is established and the mean square convergence of these methods is proved. The expectation and variance of the solution are derived. We supplement this method by plotting computational errors.

advances in difference equations

Mean square numerical solution of stochastic differential equations by fourth order Runge-Kutta method and its application in the electric circuits with noise