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

Nonlinear Analysis

Ozgur Yildirim¹  Meltem Uzun¹ 

[1] Yildiz Technical University;

关键词: existence;    uniqueness;    weak solutions;    finite difference;    fixed point theory;   

DOI  :  10.15388/namc.2020.25.20558

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown