Numerical approximation and simulation of the stochastic wave equation on the sphere

Abstract

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of the driving noise and the initial conditions. Numerical experiments confirm the theoretical rates. The developed numerical method is extended to stochastic wave equations on higher-dimensional spheres and to the free stochastic Schrödinger equation on the unit sphere.

arXiv comment26 pages, 7 figures

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Cited by in corpus (5)

• Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping
• Temporal approximation of stochastic evolution equations with irregular nonlinearities
• Pathwise Uniform Convergence of Time Discretisation Schemes for SPDEs
• Spectral approximation of a new class of stochastic fractional evolution equations
• Euler-Maruyama approximations of the stochastic heat equation on the sphere