Crank-nicolson finite difference scheme for numerical solution of generalized equal width wave (gew) equation

This thesis study, which aims to find numerical solutions of the Generalized Equal Width Wave (GEW) Equation, consists of five chapters. In the introduction chapter of the thesis, the concept of wave and wave equations are briefly mentioned. In the second chapter, the finite difference methods used in the thesis, Rubin-Graves and Richtmyer linearization techniques, von Neumann stability analysis, local truncation error, stability, consistency, convergence definitions and Lax's equivalence theorem are presented. In the third chapter, the literature review of the GEW equation is made in detail. In addition, three model problems are introduced: Single solitary wave motion, two solitary wave interaction and Maxwellian initial condition wave motion. In the fourth chapter, instead of the nonlinear term in the GEW equation, the schemes called CNSFY-I and CNSFY-II are obtained by applying the Rubin-Graves and Richtmyer linearization techniques, respectively, together with the Crank-Nicolson finite difference method. Again in the same chapter, after giving the local truncation error and stability analysis of the Crank-Nicolson finite difference scheme for this equation, the comparison of the numerical solutions obtained by applying the CNSFY-I and CNSFY-II schemes to the three model problems mentioned above with the existing exact solution and the numerical solutions in other studies in the literature is presented in the tables. In addition, figures are presented for some special selections of parameters in order to observe the behavior of the model problems. In the last chapter of the thesis, the numerical results obtained with CNSFY-I and CNSFY-II are compared with each other and their evaluations are made.