Collocation Solutions to Pseudodifferential Equations of Negative Orders on the Sphere Using Spherical Radial Basis Functions
نویسندگان
چکیده
Abstract. Spherical radial basis functions are used to define approximate solutions to pseudodifferential equations of negative orders on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the collocation method. A salient feature of our approach in this paper is a simple error analysis for the collocation method using the same argument as that for the Galerkin method.
منابع مشابه
Pseudodifferential equations on the sphere with radial basis functions: Error analysis
Spherical radial basis functions are used to define approximate solutions to strongly elliptic and elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and collocation methods. A salient feature of the paper is a unified theory for error analysis of both approximation methods.
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