The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered...

This paper presents the closed-loop composite control of singularly perturbed bilinear systems with a quadratic performance criterion, using successive Galerkin approximation(SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time and fast-time scale by the singular perturbation theory, and we obtain feedback control laws from each subsystem using SGA. We...

In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or t...

We consider the numerical solution, by a Petrov–Galerkin finite-element method, of a singularly perturbed reaction–diffusion differential equation posed on the unit square. In Lin & Stynes (2012, A balanced finite element method for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal., 50, 2729–2743), it is argued that the natural energy norm, associated with a standard Galerk...

A new family of Petrov-Galerkin nite element methods on triangular grids is constructed for singularly perturbed elliptic problems in two dimensions. It uses divergence-free trial functions that form a natural generalization of one-dimensional exponential trial functions. This family includes an improved version of the divergence-free nite element method used in the PLTMG code. Numerical result...

In magnetically confined plasma research, the understandings of small and large perturbations at equilibrium are both critical for plasma controlling and steady state operation. Numerical simulations using original MHD model can hardly give clear picture for small perturbations, while non-conservative perturbed MHD model may break conservation law, and give unphysical results when perturbations...