Department of Mathematics, Faculty of Science, Akdeniz University, TR 07058 Antalya, Turkey.
Comput Biol Chem. 2017 Apr;67:205-212. doi: 10.1016/j.compbiolchem.2016.12.006. Epub 2017 Jan 18.
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.
在这项研究中，我们考虑了一个关于 HIV 感染 CD4 T 细胞的非线性一阶模型。为了对其进行数值求解，我们提出了一种新的方法，该方法基于类似于 Galerkin 方法的指数多项式。考虑到近似解的形式为指数多项式，我们首先将这些近似解代入原始模型中。由此得到一些关系，我们用矩阵来表示这些关系。然后，将一组指数函数与这些矩阵表达式进行内积，得到一个非线性代数方程组。这些方程的解给出了模型的近似解。此外，还详细讨论了残差修正技术，该技术旨在通过估计误差来减小近似解的误差。通过一个例子说明了该方法和残差修正技术。并将结果与文献中众多现有的方法进行了比较。
