Fermat Collocation Method for Solvıng a Class of the Second Order Nonlinear Differential Equations

Abstract

In this paper, a matrix method based on collocation points on any interval [a,b] is proposed for the approximate solution of some second order nonlinear ordinary differential equations with the mixed conditions in terms of Fermat polynomials. The method, by means of collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Fermat coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and high accurate.