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Numerical solution of stochastic differential equations by second order Runge-Kutta methods. (English) Zbl 1219.65009

Summary: We propose the numerical solutions of stochastic initial value problems via random Runge-Kutta methods of the second order and mean square convergence of these methods is proved. A random mean value theorem is required and established. The concept of mean square modulus of continuity is also introduced. Expectation and variance of the approximating process are computed. Numerical examples show that the approximate solutions have a good degree of accuracy.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
34F05 Ordinary differential equations and systems with randomness
60H25 Random operators and equations (aspects of stochastic analysis)
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