Numerical solutions of modified equal width wave equation with finite elements method

This Ph.D. thesis consists of five chapters. In the first chapter,after giving general information about the numerical methods such as finitedifference, variatonal, weighted residual and finite elements method,fundamental concepts about spline and B-spline basis functions are given.Moreover, Modified Equal Width Wave (MEW) equation and model problems of whichsolutions are sought throughout the thesis are introduced.The second, third, fourth and fifth chapters constitute the orijinalparts of this thesis. In the second chapter, numerical solutions of the MEWequation are obtained by Galerkin finite element method with quadratic andcubic B-spline functions. This method is applied to two model problems givenin Chapter 1. The obtained numerical results are compared with existingresults in the literature and the invariants denoted by $I_{1},$ $I_{2}$ and$I_{3}$ and the error norms $L_{2\text{ }}$and $L_{\infty\text{ }}$are givenin the form of tables.In the third chapter, numerical solutions of the MEW equation areobtained by Petrov-Galerkin finite element method with linear,quadratic andcubic B-spline functions. This method is applied to two model problems givenin Chapter 1. The obtained numerical results are compared with existingresults in the literature and the invariants and the error norms are given in theform of tables.In the fourth chapter, numerical solutions of the MEW equation areobtained by Subdomain finite element method with quartic and sextic B-splinefunctions. This method is applied to two model problems given in Chapter 1.The obtained numerical results are compared with existing results in theliterature and the invariants and the error norms are given in the form of tables.In the fifth chapter, numerical solutions of the MEW equation areobtained by Collocation finite element method with cubic, quintic and septicB-spline functions. This method is applied to three model problemsgiven in Chapter 1. The obtained numerical results are compared with existingresults in the literature and the invariants and the error norms are given in theform of tables. Stability analysis has been made for all themethods used to obtain the numerical solutions of the MEW equation.