Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system
Articles
Ozgur Yildirim
Yildiz Technical University
https://orcid.org/0000-0003-1375-2503
Meltem Uzun
Yildiz Technical University
https://orcid.org/0000-0002-2199-8493
Published 2020-11-01
https://doi.org/10.15388/namc.2020.25.20558
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Keywords

existence
uniqueness
weak solutions
finite difference
fixed point theory

How to Cite

Yildirim O. and Uzun M. (2020) “Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system”, Nonlinear Analysis: Modelling and Control, 25(6), pp. 997-1014. doi: 10.15388/namc.2020.25.20558.

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.

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