Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: In this paper, the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces has been proved, and the generalized stability has been shown for the generalized additive-CUBIC-QUARTIC functional equation.
Abstract: In this paper, we consider the additive-cubic-quartic functional equation and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces.
67 citations
TL;DR: In this article, the authors considered the linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces, where the optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE).
Abstract: The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
67 citations
TL;DR: In this paper, the derivation of superposition rules, which express the general solution of ordinary differential equations, is studied in terms of a finite number of particular solutions, where the point of departure is Lie's criterion according to which such a rule exists if and only if the vector fields η (x, t ). ∇ generate a finite dimensional Lie algebra.
67 citations
TL;DR: A hybrid method which combines the Adomian decomposition method, the Laplace transform algorithm and the Pade approximant is introduced to solve the approximate analytic solutions of the nonlinear Riccati differential equations.
Abstract: In this paper, a hybrid method which combines the Adomian decomposition method (ADM), the Laplace transform algorithm and the Pade approximant is introduced to solve the approximate analytic solutions of the nonlinear Riccati differential equations. This hybrid method demonstrates accurate and reliable results, and has a great improvement in the ADM truncated series solution which diverges rapidly as the applicable domain increases. Three examples herein are given to demonstrate good accuracy and fast convergence in comparison with the exact solution.
66 citations
TL;DR: In this paper, a relationship between the massless a2(2) integrable quantum field theory and a certain third-order ordinary differential equation was established, and a non-linear integral equation for the generalised spectral problem was derived, and some numerical checks were performed.
66 citations