Zhang Wei-Jiang

Asymptotic method of travelling wave solutions for a class of nonlinear reaction diffusion equation

Abstract In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.

Exponential dichotomies of nonlinear discrete systems and its application to numerical analysis and computation

In this pepar we consider the upwind difference scheme of a kind of boundary value problems for nonlinear, second order, ordinary differential equations. Singular perturbation method is applied to construct the asymptotic approximation of the solution to the upwind difference equation. Using the theory of exponential dichotomies we show that the solution of an order-reduced equation is a good approximation of the solution to the upwind difference equation except near boundaries. We construct correctors which yield asymptotic approximations by adding them to the solution of the order-reduced equation. Finally, some numerical examples are illustrated.

Disturbance-Resistibility of Singularly Perturbed Linear Systems

Abstract A disturbance-resistibility problem of singularly perturbed linear systems with low-frequency and high-frequency modes is analyzed. The conditions for disturbance resistance of singularly perturbed linear systems by state feedback are given. The decomposition of the low-frequency and high-frequency modes and the nonsingular transformation of coordinates are employed to show that the disturbance resistance of the slow and fast subsystems by state feedback can ensure that the effect of disturbance on the output of the original system is O(∊).