In this paper, the Exp-function method is used to seek new generalized solitonary solutions of the Riccati equation. Based on the Riccati equation and one of its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional dispersive long wave equations are obtained. Compared with the tanh-function method and its extensions, the proposed method i...

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtaine...

In this paper, we introduce an efficient method for solving the quadratic Riccati differential equation. In this technique, combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm to the exact solution of the nonlinear Riccati equation. Unlike the previous approach for this problem, so-called NHPM, the present method, does not need the init...

When Newton’s method is applied to find the maximal symmetric solution of a discrete algebraic Riccati equation (DARE), convergence can be guaranteed under moderate conditions. In particular, the initial guess does not need to be close to the solution. The convergence is quadratic if the Fréchet derivative is invertible at the solution. When the closed-loop matrix has eigenvalues on the unit ci...

where α > 0, qn ≥ 0, 0 ≤ pn ≤ p < ∞. By using Riccati transformation we establish some new sufficient conditions which ensure that every solution of equation (E) is either oscillatory or converges to zero. These results improve some known results in the literature. Examples are provided to illustrate the main results. 2000 AMS Subjects Classification: 39A10

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given and rate of convergence ...

In this article, we use the Riccati transformation technique and some inequalities, to establish oscillation theorems for all solutions to evenorder quasilinear neutral differential equation “ˆ` x(t) + p(t)x(τ(t)) ́(n−1) ̃γ”′ + q(t)x ` σ(t) ́ = 0, t ≥ t0. Our main results are illustrated with examples.