turkmath.org

In this study two-dimensional sine-Gordon equation is solved by using the dual reciprocity boundary element method (DRBEM). At the beginning of the solution procedure, central difference approximations are used for both first and second order time derivatives. After inserting the finite difference approximations into the governing equation, the form of the modified Helmholtz equation is obtained. The fundamental solution of modified Helmholtz equation is employed in the integral equation formulation. The inhomogeneous terms of the equation cause a domain integral in the integral equation formulation which leads to loss of advantage of the method. The DRBEM provides to transform the domain integral into the boundary integral by approximating the inhomogeneous term of the equation with thin plate spline ($r^2ln\,r$). First, code validation of the method is done using a test problem and then proposed method is applied for several cases involving line and ring solitons to show its capability to treat of the problem. Presented numerical results are observed to be in good agreement with other numerical results available in the literature.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1615194140427?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d