A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise u...

This paper addresses the problem of designing an H∞ filter for a class of nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a fuzzy H∞ filter that guarantees the L2-gain from an exogenous input to a filter error to be less than or equal to a prescribed value. In order to alleviate the ill-conditio...

Singularly perturbed vector nonlinear Schrödinger equations (PVNLS) are investigated. Emphasis is placed upon the relation with their restriction: The singularly perturbed scalar nonlinear Schrödinger equation (PNLS) studied in [10]. It turns out that the persistent homoclinic orbit for the PNLS [10] is the only one for the PVNLS, asymptotic to the same saddle.

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform backward Euler used temporal Furthermore, preconditioning approach is also to ensure uniform convergence. Numerical experiments show that method first-order accuracy in time almost space.

This paper is concerned with a semi-linear elliptic problem Robin boundary condition: style='text-indent:20px;'> \begin{document}$ \begin{equation} \left\{\begin{array}{lll} \varepsilon \Delta w-\lambda w^{1+\chi} = 0, &\text{in} \ \Omega\\ \nabla w \cdot \vec{n}+\gamma & \text{on} \partial \Omega \end{array}\right...