We propose and analyse a method based on the Riccati transformation for solving the evolutionary Hamilton–Jacobi–Bellman equation arising from the dynamic stochastic optimal allocation problem. We show how the fully nonlinear Hamilton–Jacobi– Bellman equation can be transformed into a quasilinear parabolic equation whose diffusion function is obtained as the value function of a certain parametr...

Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ(x) with χ(x) being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi eq...

We introduce and prove some new interval oscillation criteria for a general class of forced second-order differential equations (E) : ( r(t)k1(x, x′) )′ + p(t)k2(x, x′)x′ + q(t)f(x) = e(t), t ≥ t0, where the functions k1(u, v), k2(u, v) and f(u) satisfy some general conditions. Our interval oscillation criteria and their proofs are different than previously published ones, and it is based on (i...

In recent years, nonlinear phenomena play a crucial role in appliedmathematics and physics. Directly searching for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive partly due to the availability of computer symbolic systems like Mathematica or Maple that allow us to perform some complicated and tedious algebraic calculation on a computer as ...

‎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 an...

In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

A new discretization based solution to the sampled-data H 1 control problem is given. In contrast to previous solution procedures, the method is not based on the lifting technique. Instead, an equivalent nite-dimensional discrete problem representation is derived directly from a description of the sampled-data system. This is achieved via a closed-loop expression of the worst-case intersample d...

We study the nonsymmetric algebraic Riccati equation whose four coefficient matrices are the blocks of a nonsingular M -matrix or an irreducible singular M -matrix M . The solution of practical interest is the minimal nonnegative solution. We show that Newton’s method with zero initial guess can be used to find this solution without any further assumptions. We also present a qualitative perturb...

In this paper, new upper matrix bounds for the solution of the continuous algebraic Riccati equation (CARE) are derived. Following the derivation of each bound, iterative algorithms are developed for obtaining sharper solution estimates. These bounds improve the restriction of the results proposed in a previous paper, and are more general. The proposed bounds are always calculated if the stabil...