Open Access

ARTICLE

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:

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

Received 05 July 2020; Accepted 21 September 2020; Issue published 22 December 2020

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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Keywords

Helmholtz equation; Chebyshev interpolation nodes; Barycentric Lagrange interpolation; meshless collocation method; high wave number; variable wave number

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Citations