On the Solution of Periodic Abel's Differential Equations of the First Kind

Abstract

In this paper, an alternative method shall be presented for the approximation of periodic Abel’s Differential Equation (ADE) of the first kind. The periodic ADE that shall be con-sidered here are those that do not have a closed form (exact) solution (even though the solution of such equations is known to exist). First, the Theorems of shall be employed to test for the existence of such solutions. Second, if such solutions exist (even though not in closed form), then a three-step hybrid method shall be derived for their approxima-tions. Furthermore, the approximate solutions obtained using the three-step method are juxtaposed with those of the conventional fourth order Runge–Kutta method to test its computational reliability. The basic properties of the method derived are also analyzed.