Open AccessNonstandard finite difference method for solving the multi-strain TB model
Author(s) -
N. H. Sweilam,
Iman A. Soliman,
S.M. AL–Mekhlafi
Publication year - 2017
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2016.10.004
Subject(s) - mathematics , euler method , stability (learning theory) , runge–kutta methods , backward euler method , numerical analysis , euler's formula , finite difference , finite difference method , numerical stability , class (philosophy) , mathematical analysis , euler equations , computer science , machine learning , artificial intelligence
In this paper, numerical studies for the mathematical model of tuberculosis (TB), that incorporates three strains, i.e., drug - sensitive, emerging multi - drug resistant(MDR) and extensively drug - resistant (XDR), are presented. Special class of numerical methods, known as nonstandard finite difference method (NSFDM) is introduced to solve this model. Numerical stability analysis of fixed points are studied. The obtained results by NSFDM are compared with other known numerical methods such as implicit Euler method and fourth-order Runge–Kutta method (RK4). It is concluded that NSFD scheme preserves the positivity of the solution and numerical stability in larger region than the other methods