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The RBF partition of unity method for solving the Klein-Gordon equation

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A Correction to this article was published on 13 November 2020

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Abstract

In this paper, a localized radial basis function (RBF) method is applied to obtain a global approximation of the solution of two dimensional Klein-Gordon equation on a given bounded domain. We use the RBF partition of unity (RBF-PU) method which is based on partitioning the original domain to several patches and using the RBF approximation on each local domain. Low computational cost and well conditioned final linear system are the main advantages of this method comparing with the original (global) RBF techniques. Numerical experiments show that the given problem could be solved successfully with a reasonable accuracy.

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Acknowledgements

Special thanks go to Dr. Davoud Mirzaei for his helpful comments and suggestions that improved the quality of the paper. Supports from IPM-Isfahan are greatly acknowledged. The author is very grateful to reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.

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  1. Department of Applied Mathematics Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran

    Mohammadreza Ahmadi Darani

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  1. Mohammadreza Ahmadi Darani
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Correspondence to Mohammadreza Ahmadi Darani.

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Ahmadi Darani, M. The RBF partition of unity method for solving the Klein-Gordon equation. Engineering with Computers 38 (Suppl 1), 679–691 (2022). https://doi.org/10.1007/s00366-020-01171-z

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