On the Numerical Solutions of the Abel's Differential Equation by Pade Series

Abstract

In this paper, we propose a matrix method to solve the Abel's differential equation in terms of Taylor polynomials and a formula for calculation of mth order derivative of y(n). Moreover, numerical solutions of Abel's differential equation has been presented by Pade approximation. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equation. Comparing the method with some known techniques indicates that the present approach is relatively easy and highly accurate.