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Solutions to the stochastic wave equation on the unit sphere are approximatedby spectral methods. Strong, weak, and almost sure convergence rates for theproposed numerical schemes are provided and shown to depend only on thesmoothness of the driving noise and the initial conditions. Numericalexperiments confirm the theoretical rates. The developed numerical method isextended to stochastic wave equations on higher-dimensional spheres and to thefree stochastic Schr\"odinger equation on the unit sphere.

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