An exponential Galerkin method for solutions of HIV infection model of CD4+ T-cells

YÜZBAŞI Ş., KARAÇAYIR M.

COMPUTATIONAL BIOLOGY AND CHEMISTRY, vol.67, pp.205-212, 2017 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 67
  • Publication Date: 2017
  • Doi Number: 10.1016/j.compbiolchem.2016.12.006
  • Journal Name: COMPUTATIONAL BIOLOGY AND CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.205-212
  • Keywords: HIV infection of CD4+ T-cells, Systems of nonlinear differential equations, Galerkin method, Inner product, Exponential polynomials, DYNAMICS, SOLVE
  • Akdeniz University Affiliated: Yes

Abstract

In this study, we consider a nonlinear first order model about the infection of CD4+ T-cells by HIV. In order to solve it numerically, we present a new method based on exponential polynomials reminiscent of the Galerkin method. Considering the approximate solutions in the form of exponential polynomials, we first substitute these approximate solutions in the original model. Some relations are thus obtained, which we express in terms of matrices. Taking inner product of a set of exponential functions with these matrix expressions then yields a nonlinear system of algebraic equations. The solution of these equations gives the approximate solutions of the model. Additionally, the technique of residual correction, which aims to reduce the error of the approximate solution by estimating this error, is discussed in some detail. The method and the residual correction technique are illustrated with an example. The results are also compared with numerous existing methods from the literature.(C) 2016 Elsevier Ltd. All rights reserved.