This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined...

Mimetic discretizations based on the support-operators methodology are derived for non-orthogonal locally refined quadrilateral meshes. The second-order convergence rate on non-smooth meshes is verified with numerical examples. 2004 Elsevier Inc. All rights reserved. PACS: 65N06; 65N22; 80A20

We do the numerical analysis and simulations for the time fractional radial diffusion equation used to describe the anomalous subdiffusive transport processes on the symmetric diffusive field. Based on rewriting the equation in a new form, we first present two kinds of implicit finite difference schemes for numerically solving the equation. Then we strictly establish the stability and convergen...

The velocity, shear-rate, variable viscosity, and variable power-law index profiles are calculated for non-Newtonian fluids using the finite difference method. The calculations are carried out for an actual viscosity function obtained by a cilrve fit through measured data and for the corresponding power law model, the simplest and most often used form for non­ Newtonian viscosity function appro...

In this paper, we consider the Darboux problem for a (1+1)dimensional cubic nonlinear Klein-Gordon equation with an external source. Stable finite difference scheme is constructed on a four-point stencil, which does not require additional iterations for passing from one level to another. It is proved, that the finite difference scheme converges with the rate O(h2), when the exact solution belon...

We propose a finite difference scheme for the Heisenberg equation and the LandauLifshitz equation. These equations have a length-preserving property and energy conservation or dissipation property. Our proposed scheme inherits both characteristic properties. We also show that the boundedness of finite difference solutions and an unique solvability of our scheme. Finally, we show some numerical ...

Abstract—This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parame...

Abstract: Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of comp...

Cheng Wang, Jian-Guo Liu, Hans Johnston 1 Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA; e-mail: [email protected] 2 Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742, USA; e-mail: [email protected] 3 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA; e-mail: hansjo...

A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational ...