Error analysis of the exponential wave integrator sine pseudo-spectral method for the higher-order Boussinesq equation


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Çanak M. C., Muslu G. M.

Numerical Algorithms, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1007/s11075-024-01763-6
  • Journal Name: Numerical Algorithms
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Keywords: Error estimate, Exponential integrator, Higher-order Boussinesq equation, Long-time dynamics, Sine pseudo-spectral method
  • Istanbul Technical University Affiliated: Yes

Abstract

In this paper, we derive a new exponential wave integrator sine pseudo-spectral (EWI-SP) method for the higher-order Boussinesq equation involving the higher-order effects of dispersion. The method is fully-explicit and it has fourth order accuracy in time and spectral accuracy in space. We rigorously carry out error analysis and establish error bounds in the Sobolev spaces. The performance of the EWI-SP method is illustrated by examining the long-time evolution of the single solitary wave, single wave splitting, and head-on collision of solitary waves. Numerical experiments confirm the theoretical results.