School of Mathematics, Iran University of Science and Technology, Tehran, Iran
Abstract
Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems. They are often referred to as a meshfree method and can be spectrally accurate. In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion. We develop our approach in two-dimensional spaces for solving Helmholtz equations. In this paper, the eigenfunction expansions are rebuilt based on Chebyshev polynomials which are more suitable in numerical computations. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method for solving two-dimensional Helmholtz equations.
Rashidinia, J., & Khasi, M. (2019). Stable Gaussian radial basis function method for solving Helmholtz equations. Computational Methods for Differential Equations, 7(1), 138-151.
MLA
Jalil Rashidinia; Manoochehr Khasi. "Stable Gaussian radial basis function method for solving Helmholtz equations". Computational Methods for Differential Equations, 7, 1, 2019, 138-151.
HARVARD
Rashidinia, J., Khasi, M. (2019). 'Stable Gaussian radial basis function method for solving Helmholtz equations', Computational Methods for Differential Equations, 7(1), pp. 138-151.
VANCOUVER
Rashidinia, J., Khasi, M. Stable Gaussian radial basis function method for solving Helmholtz equations. Computational Methods for Differential Equations, 2019; 7(1): 138-151.
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