Based on the finite difference method for the solution of the Rosenau-RLW equation a numerical diagram

The content of this thesis is organized as follows: In Chapter 1, a literature review is given, especially regarding the numerical studies on the 1-dimensional nonlinear general Rosenau-RLW equation, which will be discussed in the thesis. In the next chapter, that is, Chapter 2, the difference approaches to derivatives that form the basis of the numerical scheme to be presented in this study, and the basic principles in the application of the finite difference method to an initial and boundary value problem, as well as consistency, stability, convergence and Lax's equivalence theorem, are briefly mentioned. Then, a numerical diagram based on the finite difference method was created for the initial and boundary value problem given by the 1-dimensional nonlinear general Rosenau-RLW equation, which is considered as a model problem. For this purpose, first, the standard forward difference formula with first-order error term was written instead of the derivatives in the time direction seen in the equation, and the Crank-Nicolson type approach was written instead of the derivatives in the position direction, and a difference equation discretized only in the time direction was found. After this, for the discretization in the position direction, the Rubin-Graves type linearization approach with a second-order error term with respect to time was written instead of the nonlinear term in the equation, and standard central difference formulas with a second-order error term were written instead of all derivatives with respect to position, resulting in a linear algebraic equation system that can be easily applied. A discretized Crank-Nicolson type difference diagram was obtained. In Chapter 3, the diagram presented was applied to sample problems selected for some special cases of the parameters seen in the model problem. The approximate numerical results obtained (point values of the solution, average and maximum error norms, mass and energy conservation constants, order of convergence of the scheme) are presented in analytical and comparative tables with the results found by other researchers, in order to show that the current method supports the convergence rate analysis, as well as the accuracy and reliability of the scheme. given as. Additionally, some graphs were drawn to verify the continuity of the existing solutions and that they exhibited the correct physical behavior of the problem. Finally, in Chapter 4, this thesis study was concluded by giving a short conclusion and mentioning future studies. Key Words: Rosenau-RLW Equation, Finite Differences, Crank-Nicolson Type Approach, Rubin-Graves Type Linearization Technique, Stability Test