Numerical Simulation of 2D Nonlinear Sine-Gordon Soliton Waves via a DQM Based on Extended Cubic B-Splines

This work presents numerical simulation of 2D Sine-Gordon equation (SGE) via modified extended cubic B-spline DQM (MECB-DQM). The ECB works as a basis function in DQM for computing the weighting coefficients of derivatives with respect to space variables. The SGE converts into system of ODEs by using these weighting coefficients which is solved by RK(5,4) method. Both the cases of damped and undamped are chosen for numerical simulation. Obtained results are more finer than the results available in literature and initiated a better correspondence with the exact and earlier numerical solutions. The analysis of ROC is also preformed.