Numerical solution of coupled korteweg-de vries (coupled KdV) equation with SSP-Runge-Kutta differantial quadrature method

This M.Sc. thesis consists of six chapters. In the first chapter, the aim of this thesis and general information about the diferential quadrature method which is used in the thesis are given. In the second chapter, some basic concepts about waves and shallow water waves together with spline functions and B-spline functions are presented. In the third chapter, after some information about the Korteweg-de Vries (KdV) and coupled KdV equations were given, the previous studies about the coupled KdV equation were mentioned. Moreover, three model problems for the coupled KdV equation were introduced. In the fourth chapter, modified cubic B-spline diferential quadrature method (MCB-DQM) as well as the strong stability-preserving Runge-Kutta (SSP-RK43) method which are used in the thesis were presented. The fifth chapter contains the main part of the thesis. In this chapter, numerical solutions of the coupled KdV equation are obtained by MCB-DQM. This method is applied to three model problems. The obtained numerical results with the error norms L2 and L∞ and the invariants I1 and I2 were given in the form of tables. In the sixth chapter, the obtained numerical results were evaluated.