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IMI/Publicaţii/BASM/Ediţii/BASM n3(97), 2021/

Numerical Implementation of Daftardar-Gejji and Jafari Method to the Quadratic Riccati Equation

Authors: Belal Batiha and Firas Ghanim
Keywords: Daftardar-Gejji and Jafari method, Riccati equation, Variational iteration method, Adomian decomposition method; Homotopy perturbation method

Abstract

The solution of quadratic Riccati differential equations can be found by classical numerical methods like Runge-Kutta method and the forward Euler method. Batiha {\it et al.}\,\,\cite{batiha07} applied variational iteration method (VIM) for the solution of General Riccati Equation. In the paper of El-Tawil {\it et al.}\, \cite{Magdy2004} they used the Adomian decomposition method (ADM) to solve the nonlinear Riccati equation. In \cite{Abbasbandy06} Abbasbandy applied Iterated He's homotopy perturbation method for solving quadratic Riccati differential equation. In \cite{Abbasbandy06a} Abbasbandy used the Homotopy perturbation method to get an analytic solution of the quadratic Riccati differential equation, and a comparison with Adomian's decomposition method was presented. In \cite{Abbasbandy07} Abbasbandy employed VIM to find the solution of the quadratic Riccati equation by using Adomian's polynomials. Tan and Abbasbandy \cite{TanAbb06} employed the Homotopy Analysis Method (HAM) to find the solution of the quadratic Riccati equation. Batiha \cite{batiha2015} used the multistage variational iteration method (MVIM) to solve the quadratic Riccati differential equation.

Belal Batiha
Department of Mathematics, Jadara University, Irbid,
Jordan
E-mail:

Firas Ghanim
College of Sciences, University of Sharjah, Sharjah, United
Arab Emirates
E-mail:



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