Solution of Riccati Equation with Variable Co-efficient by Differential Transform Method

In this paper Differential Transform Method (DTM) is implemented to solve some Riccati differ- ential equations with variable co-efficients. This technique doesn't require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. The results derived by this method are compared with the numerical results by Runge Kutta 4 (RK4) method. odinger spectral problem by using the Cole-Hopf transformation (7). Thus Riccati equation plays an important role in the solution of various nonlinear systems. The solution of these equations can be obtained numerically by the forward Euler method and Runge-Kutta method. An unconditionally stable scheme was presented by Dubois and Saidi (8). An analytic solution of the nonlinear Riccati equation was obtained by El-Tawil et al. (9) using Adomian decomposition method. Recently, Tan and Abbasbandy (10) implemented the Homotopy Analysis Method (HAM) to solve a quadratic Riccati equation. Abbasbandy (11) also solved one example of the quadratic Riccati differential equation (with constant coefficient) by He's variational iteration method by using Adomian's polynomials. Biazar and Eslami (12) also solved the quadratic Riccati differential equation (with constant coefficient) using the Differential Transform method. Batiha et al. solved some of the Riccati equations by Variational Iteration Method (13). The concept of differential transform was first introduced by Zhou (14) in solving linear and nonlinear initial value problems in electrical circuit analysis. The traditional Taylor series method takes a long time for computation of higher order derivatives. Instead, differential transform method (DTM) is an iterative procedure for obtaining analytic Taylor series solution of differential equations and is much easier. Here we have derived the solution of some Riccati equations (with variable co-efficients) by