Nonnegativity of exact and numerical solutions of some chemotactic models

Nonstandard explicit third-order Runge-Kutta method with positivity property

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

Numerical solution for the risk of transmission of some novel coronavirus (2019-nCov) models by the Newton-Taylor polynomial solutions

In this paper we consider two type of mathematical models for the novel coronavirus (2019-nCov), which are in the form of a nonlinear differential equations system. In the first model the contact rate, , and transition rate of  symptomatic infected indeviduals to the quarantined infected class, , are constant. And in the second model these quantities are time dependent. These models are the...

Survival and Chemotactic Behavior of H pylori at Different Media pH

Background: H pylori is a human gastric pathogen. Chemotaxis is an essential factor in colonization of H pylori, but very little is known about its chemotactic responses at different pH conditions, especially in acidic environment of stomach as its natural habitant. Methods: We first determined survival of H pylori under various pH conditions in the presence and absence of urea.  Chemotaxis was...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...