Özet:
In this thesis, we investigate the existence and uniqueness of weak solutions for the system of finite difference schemes for the coupled sine-Gordon equations. The novel first order of accuracy unconditionally stable difference scheme is considered. The variational method, which is also known as the energy method is employed to prove the unique weak solvability. We also present a novel unified approach for the numerical solution of the system by combining the difference scheme with a convenient adaptation of fixed point theory. Several test problems are considered and results of the numerical experiments are provided with error analysis in order to verify the accuracy of the proposed numerical method.
