In this paper, we analyze the connections between the different qualitative properties of
numerical solutions of linear parabolic problems with Dirichlet-type boundary condition. First …

The preservation of characteristic qualitative properties of different phenomena is a more
and more important requirement in the construction of reliable numerical models. For …

In this paper we present some extensions of the classical SIR model with non-symmetric
spatial dependence. SIR-type models usually describe the epidemic in a population, which …

Criteria are developed for monotonicity of linear as well as nonlinear difference schemes
associated with the numerical analysis of systems of partial differential equations …

This article aims to compare the results obtained by applying three numerical methods:
Explicit Euler, Crank-Nicolson, and Multi-stage (R11), in the one-dimensional heat diffusion …

Many phenomena in nature can be described by mathematical models which consist of
functions of a certain number of independent variables and parameters. In particular, if some …

The monotonicity and stability of difference schemes for hyperbolic systems of conservation
laws with source terms is studied. The basic approach is to investigate the stability and …

The stability and monotonicity of nonlinear difference schemes are studied. The basic
approach is to investigate a nonlinear scheme in terms of its corresponding scheme in …

In this paper we investigate two special qualitative properties of the finite difference solutions
of one-dimensional nonlinear parabolic initial boundary value problems. The first property …

The monotonicity and stability of difference schemes for, in general, hyperbolic systems of
conservation laws with source terms are studied. The basic approach is to investigate the …