Advances in Computational Mathematics

, Volume 40, Issue 2, pp 353–375 | Cite as

Solving the heat equation on the unit sphere via Laplace transforms and radial basis functions

  • Quoc Thong Le Gia
  • William McLean


We propose a method to construct numerical solutions of parabolic equations on the unit sphere. The time discretization uses Laplace transforms and quadrature. The spatial approximation of the solution employs radial basis functions restricted to the sphere. The method allows us to construct high accuracy numerical solutions in parallel. We establish L 2 error estimates for smooth and nonsmooth initial data, and describe some numerical experiments.


Parabolic equations Laplace transforms Unit sphere Radial basis functions 

Mathematics Subject Classifications (2010)

35R01 65N30 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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