In this paper we establish the stability condition of a general class of finite difference schemes applied to nonlinear complex reaction-diffusion equations. We consider the numerical solution of both implicit and semi-implicit discretizations. To illustrate the theoretical results we present some numerical examples computed with a semi-implicit scheme applied to a nonlinear equation.

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H norm are derived. Mathematics Subject Classification. 65N06, 65N12, 65N15, 65N30. Received December 5, 2007. Revised July 21, 2008. Published online December 5, 2008.

This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form (py")" + (q r)y 0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.

In this paper, we study the behaviour of a microcantilever beam under electrostatic actuation using finite difference method. This problem has a lot of applications in MEMS based devices like accelerometers, switches and others. In this paper, we formulated the problem of a cantilever beam with proof mass at its end and carried out the finite difference solution. we studied the effects of lengt...

We present a compact high-order finite difference scheme for option pricing in the well-known Heston stochastic volatility model. The scheme is fourth order accurate in space and second order accurate in time. This is also confirmed by the numerical experiments that we present.

This paper studies the enhanced efficiency of the field strength coupled into slots by using the finite difference time domain method. The coupled field strength with the different slots shape, size, and polarization direction is assisted, some useful rules are concluded. The easiest to form enhanced efficiency of field strength is rectangular slots, square slots are the second, and the most di...

Multigrid schemes for high order finite difference methods on summationby-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserv...

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...