Bernstein collocation method for the approximate solution of a certain class of nonlinear differential equation and equation systems

This thesis consists of six chapters. The first chapter is devoted to the introduction. The second chapter deals with the preliminaries, necessary definitions that will be used in the next chapters. The original part of this study is included in the third and fourth chapter. In this section, a method is developed in terms of Bernstein polynomial solutions to have approximate solutions of nonlinear differential equations and its systems. In the fifth chapter, examples of the nonlinear differential equation and equation systems have been solved by using this method and also the error analysis and graphics are given here. In the sixth chapter, error analysis are included to demonstrate the validity and applicability of the given method.