We extend the nonstandard finite difference method of solution to the study of pharmacokinetic-pharmacodynamic models. Pharmacokinetic (PK) models are commonly used to predict drug concentrations that drive controlled intravenous (I.V.) transfers (or infusion and oral transfers) while pharmacokinetic and pharmacodynamic (PD) interaction models are used to provide predictions of drug concentrati...

We propose a new model of computation based on Nonstandard Analysis. Intuitively, the role of ‘algorithm’ is played by a new notion of finite procedure, called Ω-invariance and inspired by physics, from Nonstandard Analysis. Moreover, the role of ‘proof’ is taken up by the Transfer Principle from Nonstandard Analysis. We obtain a number of results in Constructive Reverse Mathematics to illustra...

‎in this paper‎, ‎we introduce fractional-order into a model of hiv-1 infection of cd4^+ t--cells‎. ‎we study the effect of ‎the changing the average number of viral particles $n$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎the nonstandard finite difference (nsfd) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order hiv-1‎‎i...

The obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand,...

in this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of tvd (total variation diminishing) of the solution, is proposed. this scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. schemes preserving the essential physical property of tvd are of great importance in practice. such s...

This is a revision of the paper archived previously on August 22, 2002. It corrects a mistake in Sec. 8 concerning eccentricities of graphs. From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities are the vertice...

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...

where φ, ψ ∈ L, H = −~ 2m ∆+V (~x) is essentially self-adjoint, H̄ is the closure ofH , and φ, ψ, V each carries at most a finite number of singularities and discontinuities. In flavor of physics literature, we will formulate the Feynman path integral with improper Riemann integrals. In hope that with further research we can formulate a rigorous polygonal path integral, we will also provide a No...

We show that standard mixed finite element methods for second order elliptic equations can be modified by imposing additional continuity conditions for the flux, which reduces the dimension of the space. This reduced space still gives a stable method with an optimal order of convergence. We recall our postprocessing method and the a posteriori error estimator based on this. AMS subject classifi...