Jentzen, Arnulf Higher order pathwise numerical approximations of SPDEs with additive noise. (English) Zbl 1228.65015 SIAM J. Numer. Anal. 49, No. 2, 642-667 (2011). The author considers the numerical approximation of semilinear parabolic stochastic partial differential equations (SPDEs) with additive noise in the form\[ dX_{t}=[AX_{t}+F(X_{t})]dt+BdW_{t}. \]In the equation, \(X_{t}\;\) belongs to a Hilbert space \(H,\;W_{t}\) is a Wiener process on a Hilbert space \(U,\;A\) is an unbounded linear operator, \(B\) is a bounded linear operator, \(F\) is a nonlinear operator.The main result of the article shows that pathwise convergence of the method proposed by the author has a higher order convergence rate than the Euler scheme. Reviewer: Grigori N. Milstein (Yekaterinburg) Cited in 1 ReviewCited in 19 Documents MSC: 65C30 Numerical solutions to stochastic differential and integral equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 35K58 Semilinear parabolic equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:stochastic partial differential equation; pathwise approximation; additive noise; fractional Brownian motion; Galerkin approximation; semilinear parabolic equations; Hilbert space; Wiener process; convergence PDFBibTeX XMLCite \textit{A. Jentzen}, SIAM J. Numer. Anal. 49, No. 2, 642--667 (2011; Zbl 1228.65015) Full Text: DOI