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Zbl 0919.65100
Shardlow, Tony
Numerical methods for stochastic parabolic PDEs.
(English)
[J] Numer. Funct. Anal. Optimization 20, No.1-2, 121-145 (1999). ISSN 0163-0563; ISSN 1532-2467/e

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 $$du(t)= \Biggl[{\partial^2u(t)\over\partial x^2}+ f(u(t))\Biggr] dt+ dB(t),\quad u(0)= U,$$ where $B(t)$ is a Wiener process. It concludes with a brief summary of results obtained in numerical experiments with $f=0$ and with $f= .5(u- u^3)$.
[M.D.Lax (Long Beach)]
MSC 2000:
*65C99 Numerical simulation
35K55 Nonlinear parabolic equations
65M06 Finite difference methods (IVP of PDE)
60H15 Stochastic partial differential equations
35R60 PDE with randomness
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: convergence; finite difference; nonlinear stochastic partial differential equation; initial value problem; Wiener process; numerical experiments

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