Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for Odd-Order Differential Equations

Authors

  • Xuhong Yu School of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P.R.China
  • Lusha Jin School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Zhongqing Wang School of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

DOI:

https://doi.org/10.4208/jcm.1907-m2018-0285

Keywords:

Chebyshev dual-Petrov-Galerkin method, Sobolev bi-orthogonal polynomials, odd-order differential equations, Numerical results.

Abstract

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-order equation, third-order equation, third-order KdV equation and fifth-order Kawahara equation are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions are expanded as an infinite and truncated Fourier-like series, respectively. Numerical experiments illustrate the effectiveness of the suggested approaches.

Downloads

Published

2021-06-10

Issue

Vol. 39 No. 1 (2021)

Section

Articles