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Rate of convergence of the method of fundamental solutions and hyperinterpolation for modified Helmholtz equations on the unit ball

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Abstract

Approximate solutions of boundary value problems of homogeneous modified Helmholtz equations on the unit ball are explicitly constructed by the method of fundamental solutions (MFS) with the order of approximation provided. Hyperinterpolation is used to find particular solutions of non-homogeneous equations, and the rate of convergence of solving boundary value problems of non-homogeneous equations is derived. Numerical examples are shown to demonstrate the efficiency of the methods.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nevada, Las Vegas, NV, 89154-4020, USA

    Xin Li

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  1. Xin Li
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Correspondence to Xin Li.

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Communicated by Robert Schaback.

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Li, X. Rate of convergence of the method of fundamental solutions and hyperinterpolation for modified Helmholtz equations on the unit ball. Adv Comput Math 29, 393–413 (2008). https://doi.org/10.1007/s10444-007-9056-1

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  • DOI: https://doi.org/10.1007/s10444-007-9056-1

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