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

DOI10.1007/s10444-013-9311-6zbMath1297.35254arXiv1207.4845OpenAlexW2088360309MaRDI QIDQ457688

William McLean, Quoc Thong Le Gia

Publication date: 29 September 2014

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4845

zbMATH Keywords

Laplace transformsheat equationradial basis functionsquadratureunit spheretime discretization\(L_2\) error estimates

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs on manifolds (35R01)

Related Items (6)

Numerical solution of the linear time fractional Klein-Gordon equation using transform based localized RBF method and quadrature ⋮ Numerical solution of multi-term time fractional wave diffusion equation using transform based local meshless method and quadrature ⋮ A localized transform-based meshless method for solving time fractional wave-diffusion equation ⋮ On the approximation of time-fractional telegraph equations using localized kernel-based method ⋮ A multiscale support vector regression method on spheres with data compression ⋮ Numerical solution of fractional order anomalous subdiffusion problems using radial kernels and transform

Uses Software

• DLMF

Cites Work

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• Spherical harmonics
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• Strictly Positive Definite Functions on Spheres
• Interior Estimates for Ritz-Galerkin Methods
• Numerical solution of a parabolic equation on the sphere using Laplace transforms and radial basis functions
• A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
• A necessary and sufficient condition for strictly positive definite functions on spheres
• Scattered Data Approximation

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