Discontinuous Galerkin Time Domain Methods for Acoustics and Comparison with Finite Difference Time Domain Methods

This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the syst...

We study the stability of some finite difference schemes for hyperbolic systems in two space dimensions. The grid is assumed to be cartesian, but the space steps in each direction are not necessarily equal. Our sufficient stability conditions are shown to be also necessary for one concrete example. We conclude with some numerical illustrations of our result. AMS subject classification: 65M12, 6...

We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energ...

The primary aim of this paper is to answer the question: what are the highest-order fiveor nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the oneand two-dimensional Poisson equation on uniform, quasi-uniform, and non-uniform face-to-face hyper-rectangular grids and directly prove the existence or non-...

A system of coupled singularly perturbed initial value problems with a small parameter is considered. The solution to the system have boundary layers. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform Shishkin mesh. On this mesh a hybrid finite difference scheme is proved to be almost second-order accurate, uniformly in the small parameter. Num...

We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is symmetric, definite and monotone with second order accuracy. It is also quite naturally adapted to corner singularities. A simple adaptive strategy yields competitive performance even in the severe case of intersecting interfaces.

in this paper, a chebyshev finite difference method has been proposed in order to solvenonlinear two-point boundary value problems for second order nonlinear differentialequations. a problem arising from chemical reactor theory is then considered. the approachconsists of reducing the problem to a set of algebraic equations. this method can be regardedas a non-uniform finite difference scheme. t...