By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,

| In this short note we present an observability criterion for systems whose state is governed by a matrix Riccati diierential equation and whose output is given by an aane transformation.

Abstract We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type flu...

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation reduced form the constructed by Painleve analysis. Based on transformation, some exact non-differentiable solutions are obtained. To gain more insights obtained solutions, two constrain...

| In this short note we present an observability criterion for systems whose state is governed by a matrix Riccati di erential equation and whose output is given by an a ne transformation.

In this paper, a Laplace transform decomposition algorithm (LTDA) is proposed to solve the Riccati equation. Comparisons are made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform...

This paper is concerned with rational matrix equations occuring in stochastic control that play an analogous role as the algebraic Riccati equation does in deterministic control. We will therefore sometimes refer to these equations as stochastic (algebraic) Riccati equations. A first rigorous treatment of a stochastic Riccati equation from LQ-control theory seems to have been undertaken by Wonh...