, Volume 22, Issue 4, pp 377-397

Approximation of parabolic PDEs on spheres using spherical basis functions

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Abstract

In this paper we investigate the approximation of a class of parabolic partial differential equations on the unit spheres S n⊂Rn+1 using spherical basis functions. Error estimates in the Sobolev norm are derived.

The results presented in this paper are taken from the author’s Ph.D. dissertation under supervision of Professor J.D. Ward and Professor F.J. Narcowich at Texas A&M University.
Communicated by C.A. Micchelli

AMS subject classification

35K05, 65M70, 46E22