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Title: | Solving non-strongly elliptic pseudodifferential equations on a sphere using radial basis functions | Authors: | Pham Thanh Duong Thanh Tran |
Keywords: | Elliptic pseudodifferential equation;Sphere;Radial basis function;Galerkin method;Collocation method | Issue Date: | 2015 | Publisher: | Elsevier | Journal/Book titles: | Computers & Mathematics with Applications | Series/Report no.: | Computers & Mathematics with Applications;Vol.70 (8) issue 8 | Abstract: | Non-strongly elliptic pseudodifferential equations on the unit sphere arise from geodesy. An example of equations of this type is the boundary integral reformulation of a boundary value problem with the Laplace equation in the interior domain of the unit sphere, and a Robin boundary condition. Approximate solutions with spherical radial basis functions are found by the Galerkin and collocation methods. The paper presents a unified theory for error analysis of both approximation methods. The theoretical results are corroborated by numerical experiments. It is noted that the stiffness matrix arising from the Galerkin method for this problem resembles that arising from a least squares method .1970–1983 |
URI(1): | http://epub.vgu.edu.vn/handle/dlibvgu/50 |
Appears in Collections: | ARTICLE/BOOK PUBLICATION |
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Solving non-strongly elliptic pseudodifferential equations on a sphere using radial basis functions.pdf | 453.28 kB | Adobe PDF | View/Open |
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