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A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation

Miaomiao Yang, Wentao Ma, Yongbin Ge*

Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, China

* Corresponding Author: Yongbin Ge. Email: email

Computer Modeling in Engineering & Sciences 2021, 126(1), 25-54. https://doi.org/10.32604/cmes.2021.012575

Abstract

In this paper, Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation. First of all, the interpolation basis function is applied to treat the spatial variables and their partial derivatives, and the collocation method for solving the second order differential equations is established. Secondly, the differential equations on a given test node. Finally, based on three kinds of test nodes, numerical experiments show that the present scheme can not only calculate the high wave numbers problems, but also calculate the variable wave numbers problems. In addition, the algorithm has the advantages of high calculation accuracy, good numerical stability and less time consuming.

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APA Style
Yang, M., Ma, W., Ge, Y. (2021). A meshless collocation method with barycentric lagrange interpolation for solving the helmholtz equation. Computer Modeling in Engineering & Sciences, 126(1), 25-54. https://doi.org/10.32604/cmes.2021.012575
Vancouver Style
Yang M, Ma W, Ge Y. A meshless collocation method with barycentric lagrange interpolation for solving the helmholtz equation. Comput Model Eng Sci. 2021;126(1):25-54 https://doi.org/10.32604/cmes.2021.012575
IEEE Style
M. Yang, W. Ma, and Y. Ge "A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation," Comput. Model. Eng. Sci., vol. 126, no. 1, pp. 25-54. 2021. https://doi.org/10.32604/cmes.2021.012575

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cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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