# zbMATH — the first resource for mathematics

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
Full Text:
##### 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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.