Ghorbani, Asghar; Momani, Shaher An effective variational iteration algorithm for solving Riccati differential equations. (English) Zbl 1192.65095 Appl. Math. Lett. 23, No. 8, 922-927 (2010). Summary: The piecewise variational iteration method (VIM) for solving Riccati differential equations (RDEs) provides a solution as a sequence of iterates. Therefore, its application to RDEs leads to the calculation of terms that are not needed and more time is consumed in repeated calculations for series solutions. In order to overcome these shortcomings, we propose an easy-to-use piecewise-truncated VIM algorithm for solving the RDEs. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that the new method is very effective and convenient for solving Riccati differential equations. Cited in 9 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations Keywords:piecewise-truncated variational iteration method; truncated variational iteration method; variational iteration method; Runge-Kutta method; Riccati differential equations; numerical examples; comparison of methods PDFBibTeX XMLCite \textit{A. Ghorbani} and \textit{S. Momani}, Appl. Math. Lett. 23, No. 8, 922--927 (2010; Zbl 1192.65095) Full Text: DOI References: [1] Reid, W. T., Riccati Differential Equations (1972), Academic Press: Academic Press New York · Zbl 0209.11601 [2] Carinena, J. F.; Marmo, G.; Perelomov, A. M.; Ranada, M. F., Related operators and exact solutions of Schrödinger equations, Internat. J. Modern Phys. A, 13, 4913-4929 (1998) · Zbl 0927.34065 [3] Scott, M. 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