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Numerical methods for stochastic parabolic PDEs. (English) Zbl 0919.65100

This paper presents a proof of the convergence of finite difference approximations of the solution of the nonlinear stochastic partial differential equation initial value problem of the form

du(t)= 2 u(t) x 2 + f (u(t))dt+dB(t),u(0)=U,

where B(t) is a Wiener process. It concludes with a brief summary of results obtained in numerical experiments with f=0 and with f=·5(u-u 3 ).

MSC:
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
35K55Nonlinear parabolic equations
65M06Finite difference methods (IVP of PDE)
60H15Stochastic partial differential equations
35R60PDEs with randomness, stochastic PDE
65M12Stability and convergence of numerical methods (IVP of PDE)