The aim of this paper is to design appropriate nonstandard finite difference (NSFD) schemes for two population mathematical models based on coupled nonlinear ordinary differential equations. Our work clarifies existing constructions NSFD these models, which are not in full compliance with Mickens' methodology. We select the denominator functions discrete first-order derivatives depending existe...

In this paper, we present a new model using a Fourdimensional (4D) Element-Oriented physical concepts based on a topological approach in electromagnetism. Its general finite formulation on dual staggered grids reveals a flexible Finite-Difference Time-Domain (FDTD) method with reasonable local approximating functions. This flexible FDTD method is developed without recourse to the traditional Ta...

Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect t...