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

被引：0
作者：
David Cohen
Annika Lang
机构：
[1] Chalmers University of Technology and University of Gothenburg,Department of Mathematical Sciences
来源：
Calcolo | 2022年 / 59卷
关键词：
Gaussian random fields; Karhunen–Loève expansion; Spherical harmonic functions; Stochastic partial differential equations; Stochastic wave equation; Stochastic Schrödinger equation; Sphere; Spectral Galerkin methods; Strong and weak convergence rates; Almost sure convergence; 60H15; 60H35; 65C30; 60G15; 60G60; 60G17; 33C55; 41A25;
D O I：
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摘要：
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.
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