In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stab...

The space and time discretization inherent to all FDTD schemes introduce non-physical dispersion errors, i.e. deviations of the speed of sound from the theoretical value predicted by the governing Euler differential equations. A general methodology for computing this dispersion error via straightforward numerical simulations of the FDTD schemes is presented. The method is shown to provide remar...

and Applied Analysis 3 andX E = x−uΔt (similarly we see thatX E = x−2uΔt for the two-step methods). In (7) with X being replaced by X E , we have φ n+1 − φ n (x − uΔt) Δt − νΔφ n+1 = f n+1 . (9) On the other hand, (9) can be derived by MMOC [5]. In fact, with u = (u 1 , u 2 ), let s denote the direction vector (1, u 1 , u 2 ), and define the operator d ds := 1 θ ( ∂ ∂t + u ⋅ ∇) , (10) with θ(x,...

We study the asymptotics of two space dimensional reaction-diffusion front speeds through mean zero space-time periodic shears using both analytical and numerical methods. The analysis hinges on traveling fronts and their estimates based on qualitative properties such as monotonicity and a priori integral inequalities. The computation uses an explicit second order upwind finite difference metho...

In this paper, Numerical Methods for solving ordinary differential equations, beginning with basic techniques of finite difference methods for linear boundary value problem is investigated. Numerical solution is found for the boundary value problem using finite difference method and the results are compared with analytical solution. MATLAB coding is developed for the finite difference method. T...

Dense phase pneumatic conveying has been investigated through simulation, using a discrete element approach for the granular particles and a finite difference method for the pressure field. Both horizontal and vertical conveying are studied and compared. Studies of single plugs or slugs promise to give insight into the performance of pneumatic conveying systems.

In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. ...

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems.