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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 \[ du(t)= \Biggl[{\partial^2u(t)\over\partial x^2}+ f(u(t))\Biggr] dt+ dB(t),\quad u(0)= U, \] where \(B(t)\) is a Wiener process. It concludes with a brief summary of results obtained in numerical experiments with \(f=0\) and with \(f= .5(u- u^3)\).

MSC:
65C99 Probabilistic methods, stochastic differential equations
35K55 Nonlinear parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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References:
[1] Da Prato G., Encyclopedia of Mathematics and its Applications 44 (1992)
[2] Da Prato G., London Mathematical Society Lecture Note Series 229 (1996)
[3] Davie A. M., Convergence of implicit schemes for numerical solution of parabolic stochastic partial differential equations (1996)
[4] DOI: 10.1090/S0025-5718-1992-1122067-1 · doi:10.1090/S0025-5718-1992-1122067-1
[5] Pazy A., Applied Mathematical Sciences 44 (1983)
[6] Shardlow T., Stoch. Anal. App. 17 (1999)
[7] Shardlow T., SIAM J. Num. Anal. 17 (1999)
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