10.1007/s40096-022-00498-6

Efficient sixth-order finite difference method for the two-dimensional nonlinear wave equation with variable coefficient

  • Shuaikang Wang1,
  • Yongbin Ge*1,
  1. Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, CN

Published in Issue 2022-11-29

How to Cite

Wang, S., & Ge, Y. (2022). Efficient sixth-order finite difference method for the two-dimensional nonlinear wave equation with variable coefficient. Mathematical Sciences, 18(2 (June 2024). https://doi.org/10.1007/s40096-022-00498-6
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Abstract

Abstract In this study, firstly, a sixth-order finite difference operator and correction technique of truncation error remainder are employed to construct a nonlinear high-order finite difference scheme and a linearized high-order finite difference scheme for solving the numerical solution of two-dimensional nonlinear wave equations with variable coefficients. Both new schemes have sixth-order accuracy in space and fourth-order accuracy in time. Then, the Richardson extrapolation technique is applied to obtain a numerical solution of sixth-order accuracy in both time and space. Meanwhile, the stability of the corresponding difference scheme for the linear wave equation is proved by Fourier analysis. In addition, two proposed sixth-order schemes are extended to solve the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes.

Keywords

  • Nonlinear wave equation,
  • Sixth-order finite difference scheme,
  • Linearized difference scheme,
  • Coupled sine-Gordon equations,
  • Richardson extrapolation

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