An exponential Wagner-Platen type scheme for SPDEs

Abstract

The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type approximation methods converge strongly, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1/2 or at least with strong order 1/2 - epsilon where epsilon > 0 is arbitrarily small. Recent results extend these results and show that Milstein-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1 - epsilon. It has also been shown that splitting-up approximation methods converge, under suitable assumptions, with strong order 1 to the exact solutions of such SPDEs. In this article an exponential Wagner-Platen type numerical approximation method for such SPDEs is proposed and shown to converge, under suitable assumptions, with strong order 3/2 - epsilon to the exact solutions of such SPDEs.

References in corpus (3)

• Higher order strong approximations of semilinear stochastic wave equation with additive space-time white noise
• Consistency and Stability of a Milstein-Galerkin Finite Element Scheme for Semilinear SPDE
• Numerical Solution of Stochastic Partial Differential Equations with Correlated Noise

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• Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB
• Application of Multiple Fourier-Legendre Series to Implementation of Strong Exponential Milstein and Wagner-Platen Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations
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• Strong convergence of numerical discretizations for semilinear stochastic evolution equations driven by multiplicative white noise
• A New Class of Exponential Integrators for Stochastic Differential Equations With Multiplicative Noise
• Enhancing the Order of the Milstein Scheme for Stochastic Partial Differential Equations with Commutative Noise