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On the Numerical Solutions of the Abel’s Differential Equation by Padé Series

Coskun Guler

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 . Moreover, numerical solutions of Abel’s differential equation has been presented by Padé 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.

Keywords


Abel’s differential equation; Taylor matrix method; Padé approximation; non linear differential equations

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