Approximate solutions of non-linear differantial and integral equationsby Chebysev method

In this study, Chebyshev matrix method was presented, in order to find the approximate solutions of non-linear differential and integral equations, in terms of Chebyshev polinomials for a given conditions. The equation given in the first chapter of method was transformed into the matrix equations, depending on the Chebyshev series coefficients and then a new equation system was formed by combining conditions with the matrix form. Hence, the finite Chebyshev series approach was obtained by finding the Chebyshev coefficients. The study consisted of five chapters. In the firs chapter, concepts which were the basis for the topic; in the second chapter, calculations of Chebyshev coefficients; in the third chapter, description of the problem, derivatives of unknown functions and the matrix form of the conditions, non-linear differantial equations to transform into the matrix equations and solution method of this equation; in the fourth chapter, non-linear Volterra-Fredholm integral equation to transform into the matrix equation and solution method were presented. In the last chapter, application of solution methods was given.