Extension of the Riccati Difference Equation from Robust Gradient Method

Non Standard Finite Difference Method for Quadratic Riccati Differential Equation

In this paper, we proposed an unconditionally stable NonStandard Finite Difference (NSFD) scheme to solve nonlinear Riccati differential equation. The accuracy and efficiency of the proposed scheme is verified by comparing the results with other numerical techniques such as Euler and RK-4 and semi analytical technique DTM. The obtained results show that the performance of NSFD scheme is more ac...

Riccati equation, Factorization Method and Shape Invariance

The Riccati Sub-ODE Method For Fractional Differential-difference Equations

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

Analysis of an Iteration Method for the Algebraic Riccati Equation

We consider a recently published method for solving algebraic Riccati equations. We present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem: we prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called shift parameters of the method. Our repr...

The new implicit finite difference method for the solution of time fractional advection-dispersion equation

In this paper, a numerical solution of time fractional advection-dispersion equations are presented.The new implicit nite dierence methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial dierentialequations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergenceof t...