On Approximation for Fractional Stochastic Partial Differential Equations on the Sphere

Abstract: 

This work gives the exact solution in terms of the Karhunen-Loève expansion to a fractional stochastic partial differential equation on the 2-dimensional unit sphere with fractional Brownian motion as driving noise and with random initial condition given by a fractional stochastic Cauchy problem. A numerical approximation to the solution is given by truncating the Karhunen-Loève expansion. We show the convergence rates of the truncation errors in degree and the mean square approximation errors in time. Numerical examples using an isotropic Gaussian random field as initial condition are given.

This is a joint work with Vo V. Anh (Queensland Univ. Technology & Xiangtan University), Philip Broadbridge (La Trobe University) and Andriy Olenko (La Trobe University).