ABSTRACT
This chapter represents the numerical simulation of (2 + 1) dimensional nonlinear sine–Gordon soliton waves. A hybrid cubic B-spline differential quadrature method is used for simulations. The hybrid cubic B-splines work as a basis function in differential quadrature method (DQM) for computing the weighting coefficients of derivatives with respect to space variables. By using these weighting coefficients, the (2 + 1) dimensional nonlinear sine–Gordon equation (SGE) transforms into system of ordinary differential equations (ODEs). These ODEs are solved by SSP-RK54 method. Both damped and undamped cases are selected for numerical simulations. Obtained results are better than the results available in literature and initiated a good agreement with the exact solution and earlier numerical results. The rate of convergence is also carried out.
