Legendre collocation method for solving nonlinear differential equations

This thesis consists of four chapters. In the first chapter, it is mentioned about the using areas of the polinomials and there is an introduction to the thesis. Furthermore, it is discussed about the first study of the Legendre polynomial. In the second chapter, main definitions and concepts used in the thesis are given. Original results are contained in the thirth and fourth section. In the thirth part, the matrix relations associated with the Legendre polynomials are obtained and by means of the these relations and Legendre collocations points, a new Legendre collocation method for the approximate solution of the some first order nonlinear ordinary differantial equations with variable cofficients under the mixed conditions is proposed. In the fourth section, examples of these kinds of equations were solved by using this new method, error analysis was done and graphics were drawn. In addition, we conclude that this new method works well and it can be suitable by examining error analysis of examples.