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Mathematics, Vol. 11, Pages 4690: Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D
Mathematics doi: 10.3390/math11224690
Authors: Anup Lamichhane Balaram Khatri Ghimire Thir Dangal
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.
