Euler–Maruyama approximations of the stochastic heat equation on the sphere
Annika Lang,
Ioanna Motschan-Armen
Abstract:The stochastic heat equation on a sphere driven by additive isotropic Wiener noise is approximated by a spectral method in space and forward and backward Euler-Maruyama schemes in time. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. Optimal strong convergence rates for a given regularity of the initial condition and driving noise are derived for the Euler-Maruyama methods. Besides strong convergence, convergence of the expectation a… Show more
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