An improved approximate analytic solution for Riccati equations over extended intervals

Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation

“…Many authors have proposed various numerical methods to solve Equations ( 1) and (2). For instance, piecewise variational iteration method in Ghorbani and Momani's [5] study, differential transform method in Biazar and Eslami's [4] study, cubic B-spline scaling functions and Chebyshev cardinal functions in Lakestani and Dehghan's [6] study, application of optimal homotopy asymptotic method in Mabood et al's [7] study, combination of Laplace transform and new homotopy perturbation methods in Vahidi et al's [8] study, Legendre scaling functions in Baghchehjoughi et al's [9] study, Lie group method and Runge-Kutta fourth-order method in Altoum's [10] study, fourth-order Runge-Kutta method in File and Aga's [11] study, the Bezier curves method in Ghomanjani and Khorram's [12] study, a weighted type of Adams-Bashforth rules in Masjed-Jamei and Shayegan's [13] study, and the fifth order predictor corrector method in Kiltu et al's [14] study. The classical fourth-order Runge-Kutta method is widely used for solving quadratic Riccati differential equations.…”

A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains

“…Because of its emergence in various applications, a significant number of works has been devoted to the analytical and approximate solution of the RDE in the last decades. For example, methods such as the Adomian's decomposition (Momani and Shawagfeh 2006), homotopy perturbation (Hosseinnia et al 2008;Odibat and Momani 2008;Khan et al 2011), variational iteration (Abbasbandy 2007;Geng et al 2009;Jafari and Tajadodi 2010), Bernstein polynomials (Yüzbasi 2013), wavelet (Abd-Elhameed and Youssri 2014; Wang et al 2017;Mohammadi and Hosseini 2011;Momani and Shawagfeh 2006;Balaji 2014), reproducing kernel Hilbert space (Sakar 2017;Sakar et al 2017;, Taylor series expansion (Aminkhah and Hemmatnezhad 2010), fractional Chebyshev finite difference (Khader 2013), Laplace-Adomian-Pade (Tsai and Chen 2010), Taylor matrix (Gülsu and Sezer 2006), artificial neural networks (Raja et al 2015) and Laplace Adomian decomposition (Vahidi et al 2014) are used to find the approximate solution of the FRDE.…”

Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains

“…Several investigators have proposed a variety of approaches to solve the Riccati equation, approximately [19][20][21][22][23][24]. In order to obtain the global approximate solution of the Riccati equation, we combine the Padé approximant of the near-field approximation as derived from the ADM with the far-field approximation as derived from the AADM [25][26][27][28] to overcome the difficulty of a finite domain of convergence.…”