Solving Classical Nonlinear Riccati Differential Equations (RDEs) Using Differential Transformation Method (DTM)

Abstract

In this paper, the Differential Transformation Method (DTM) is used to solve nonlinear Riccatti differential equation of the form:
\begin{equation}\label{GrindEQ__1_}
\left(\frac{dj}{dt} \right)^{\beta } =S(t)j+Q(t)j^{2} +R(t), 0\le t\le 1
\end{equation}
Subject to initial condition $j(0)=A$, where $S(t), Q(t), R(t), A$ are constant variables and when $\beta =1$, the above equation \eqref{GrindEQ__1_} is called Classical Riccati differential equation. The principle of differential transformation method is briefly introduced and applied for the first derivation of the set of nonlinear Riccatti differential equations. Accuracy and efficiency of the proposed method is verified through numerical examples. The result obtained with the proposed method are in good agreement with exact solution of the problem considered. The method is simply and efficient as numerical tool for any other class of the differential equations.