Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

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YILDIRIM Ö., UZUN M.

NONLINEAR ANALYSIS-MODELLING AND CONTROL, vol.25, no.6, pp.997-1014, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.15388/namc.2020.25.20558
  • Journal Name: NONLINEAR ANALYSIS-MODELLING AND CONTROL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.997-1014
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability. We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.