Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D

Anup Lamichhane (), Balaram Khatri Ghimire and Thir Dangal
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Anup Lamichhane: School of Science, Technology, and Mathematics, Ohio Northern University, Ada, OH 45810, USA
Balaram Khatri Ghimire: Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 39104, USA
Thir Dangal: Department of Mathematics, Augusta University, Augusta, GA 30912, USA

Mathematics, 2023, vol. 11, issue 22, 1-15

Abstract: Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale problems, but this method is numerically less accurate. In this paper, we propose a numerical scheme to improve the accuracy of the L-ORBFs by adding low-degree polynomials in the localized collocation process. The numerical results validate that the proposed numerical scheme is highly accurate and clearly outperforms the results of the L-ORBFs.

Keywords: augmented polynomials; localized collocation method; oscillatory radial basis functions; particular solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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