In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross–coupled algebraic Riccati equations with a small positive parameter ε. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov equation direct method, to solve the cross–co...

In this paper a singularly perturbed reaction-diffusion equation with a discontinuous source term is examined. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented which validate the theoretical results.

A linear time dependent singularly perturbed convection-diffusion problem is examined. The convective coefficient contains an interior layer (with a hyperbolic tangent profile), which in turn induces an interior layer in the solution. A numerical method consisting of a monotone finite difference operator and a piecewise-uniform Shishkin mesh is constructed and analysed. Neglecting logarithmic f...

We give a new proof that the El-Mistikawy and Werle finite-difference scheme is uniformly second-order accurate for a nonselfadjoint singularly perturbed boundary value problem. To do this, we use exponential finite elements and a discretized Green's function. The proof is direct, gives the nodal errors explicitly in integral form, and involves much less computation than in previous proofs of t...

We consider smooth systems limiting as ? ? 0 to piecewise-smooth (PWS) with a boundary-focus (BF) bifurcation. After deriving suitable local normal form, we study the dynamics for system sufficiently small but non-zero , using combination of geometric singular perturbation theory and blow-up . show that type BF bifurcation in PWS determines structure within an ?dependent domain which shrinks ze...

In this article, we deal with some problems involving a class of singularly perturbed elliptic operators. We prove the asymptotic preserving general Galerkin method associated to semilinear problem. use particular approximation estimate convergence rate on whole domain, for linear Finally, study behaviour semigroup generated.

This paper presents a standard H∞ controller design for singularly perturbed systems with frequency domain by unified approach using the delta operators. Decomposition of the singularly perturbed systems into the fast and slow subsystems is shown. And the delta operator approach is implemented to improve a finite word-length (FWL) characteristics. The delta operator systems have the better FWL ...

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H-norm for a singularly perturbed syste...