Shifted Lagrangian Jacobi collocation scheme for numerical solution of a model of HIV infection

Autores: Sobhan Latifi, Mohammad M. Moayeri
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 75, Nº. 3, 2018, págs. 379-398
Idioma: inglés
DOI: 10.1007/s40324-017-0138-9
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Resumen
- In this paper, a system of nonlinear ordinary differential equations (NODEs), namely the equation model of the human immunodeficiency virus (HIV) infection of CD4+T cells, is studied. Our approach is implemented by using the Shifted-Lagrangian Jacobi (SLJ) polynomials formed by Shifted-Jacobi-Gauss-Radau (SJ-GR) points. In a new insight, by applying Quasilinearization method (QLM) the system of NODE’s is simplified and changed into a system of Linear ordinary differential equations (LODE’s) and instead of working on a system of NODE’s, all processes and works are done on a system of LODE’s. Therefore, unlike the most of the current studies working on nonlinear algebraic equations, the problem is reduced to a system of linear algebraic equations. Then, to solve the problem and find the unknown approximation coefficients, a system of Ax=b has been solved. At the end, the accuracy and reliability of this method are shown and comparisons with the other current work’s results are made.