Implementation of DRBEM for coupled sine-Gordon equations

Abstract

In this study, two-dimensional, time dependent, nonlinear, coupled sine-Gordon equations (CSGE) is solved using the dual reciprocity boundary element method (DRBEM). The DRBEM provides to transform the domain integral, caused by the inhomogeneous terms, into the boundary integral by approximating with thin plate spline. DRBEM formulation is derived using the fundamental solution of the modified Helmholtz equations (MHE)’s. In order to write the original equations in the form of MHE, time dervatives are expanded using finite difference. The principle purpose of this study is to show that DRBEM is a successful alternative for the solution of CSGE. Method is tested with the examples which have the analitical solution. The study also includes the solutions of other examples in the literature. Numerical experiments show that obtained results are in good agreement with other studies where the problem has been solved before and thus DRBEM is effective and accurate for the solution of CSGE.