Convergence of a Runge-Kutta scheme for the numerical solution of stochastic partial differential equations

We consider the numerical solutions of nonlinear parabolic stochastic partial differential equations (SPDEs)driven by additive white noise. We estimate the numerical solution in the L1() topology by a numerical method whichis based on the Taylor expansions of solutions of stochasticpartial differential equations with additive noise, and in thatway one could call the scheme used here a Runge-Kutta schemefor SPDEs. We show convergence of this method and numericalexample gives insight into the reliability of the theoretical study.

کلیدواژه ها:

Stochastic partial differential equations ، Convergence ، Pathwise approximation