Numerical solution of a parabolic equation on the sphere using Laplace transforms and radial basis functions

Quoc Thong Le Gia, William McLean


We propose a method to construct numerical solutions of a parabolic equation on the unit sphere. The time discretisation uses Laplace transformation and quadrature. The spatial approximation employs radial basis functions restricted to the sphere. The method provides a parallel algorithm to construct high accuracy numerical solutions.

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parabolic equation, radial basis function, unit sphere

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