an:01279316
Zbl 0919.65100
Shardlow, Tony
Numerical methods for stochastic parabolic PDEs
EN
Numer. Funct. Anal. Optimization 20, No. 1-2, 121-145 (1999).
00053657
1999
j
65C99 35K55 65M06 60H15 35R60 65M12
convergence; finite difference; nonlinear stochastic partial differential equation; initial value problem; Wiener process; numerical experiments
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)