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, it was shown that every continuous function is a weak solution of the uniform limits of a continuous function and that every function is monotone if it is monotonous.
Abstract: REMARK 1. From the proof, it will be clear that we can in addition ensure that y(tj) — y(tj) for any sequence (tj) of distinct real numbers such that \\tj\\ —* °° as ƒ —> oo. REMARK 2. We may moreover make y monotone if
62 citations
TL;DR: The asymptotic structure of composite mode-dependent controller is characterized, which shows that the controller is independent of the singular perturbation @e, when @e is sufficiently small.
62 citations
TL;DR: In this article, a Lie group analysis is used to carry out the similarity reduction and exact solutions of the 3+1)-dimensional modified KdV-Zakharov-Kuznetsov equation.
Abstract: In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the \((3+1)\)-dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new partial differential equation with less number of independent variables, and again using Lie group symmetry method, the new partial differential equation is reduced into an ordinary differential equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV–ZK equation. In addition to that, solitary wave solutions of the mKdV–ZK equation are derived from the reduction equation. Thus, we obtain some new exact explicit solutions of the \((3+1)\)-dimensional mKdV–ZK equation which describes the dynamics of nonlinear waves in plasmas.
62 citations
62 citations
TL;DR: In this paper, a general defect-correction method is proposed and numerical examples are given for the use of this method in combination with A. Bunse-Gerstner and V. Mehrmann's (1986) SR method.
Abstract: The solution of discrete and continuous algebraic Riccati equations is considered. It is shown that if an approximate solution is obtained, then the defect for this solution again solves an algebraic Riccati equation of the same form, and that the system properties of detectability and stabilizability are inherited by this defect equation. On the basis of these results, a general defect-correction method is proposed and numerical examples are given for the use of this method in combination with A. Bunse-Gerstner and V. Mehrmann's (1986) SR method. >
62 citations