EULER AND TAYLOR POLYNOMIALS METHOD FOR SOLVING VOLTERRA TYPE INTEGRO DIFFERENTIAL EQUATIONS WITH NONLINEAR TERMS

In this study, the first order nonlinear Volterra type integro-differential equations are used in order to identify approximate solutions concerning Euler polynomials of a matrix method based on collocation points. This method converts the mentioned nonlinear integro-differential equation into the matrix equation with the utilization of Euler polynomials along with collocation points. The matrix equation is a system of nonlinear algebraic equations with the unknown Euler coefficients. Additionally, this approach provides analytic solutions, if the exact solutions are polynomials. Furthermore, some illustrative examples are presented with the aid of an error estimation by using the Mean-Value Theorem and residual functions. The obtained results show that the developed method is efficient and simple enough to be applied. And also, convergence of the solutions of the problems were examined. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB.