Numerical solution of 1-dimensional regularized long wave equation

This thesis consists of six chapters. In the first chapter, a literature review on the RLW equation is given and the basic concepts and theorems used in the thesis are given. In the second chapter, finite difference approximations and some of the single and multi-step methods for a well-defined initial value problem are discussed. In the third chapter, test problems for which numerical solutions of the RLW equation are obtained are defined and the conservation constants are given. In the fourth section, the RLW equation is discretized according to the Crank-Nicolson method. Then the nonlinear term is linearized by Rubin-Graves linearization and a numerical scheme is obtained by applying finite difference approximations. With the obtained numerical scheme, numerical solutions of the test problems were found. In the fifth section, the RLW equation is discretized according to the Adams-Bashforth method. Then, two numerical schemes were obtained by applying finite difference approximations. With the obtained numerical schemes, numerical solutions of the test problems were found. Finally, in the sixth section, the results are evaluated by comparing the obtained schemes. Keywords: Regularized Long Wave Equation, Finite Differences, Multistep Methods