A fast Taylor-wavelet based numerical algorithm for the solution of HIV-infected $\mathrm{CD4}^{+} \mathrm{T}$ cells model

Abstract

In this article, we present a novel approach under the Taylor wavelet and collocation technique which is computationally efficient to obtain the solution of the model of $\mathrm{CD4}^{+} \mathrm{T}$ cells of HIV infection. A system of nonlinear ordinary differential equations represents this mathematical model. On applying the proposed technique described in this article, we have transformed this model into algebraic form and then simplified using a suitable method. The suggested Taylor wavelet approach is worked out for the convergence analysis and thereafter it is also demonstrated that the Taylor wavelet expansion of a function converges uniformly to itself. It is anticipated that the proposed approach would be more efficient and suitable for solving a variety of nonlinear ordinary and partial differential equations that occur in various such models of medical science and engineering. Tables and graphs are included to show how the suggested wavelet method provides enhanced accuracy for a wide range of problems. Relative data and computations are performed over MATLAB software.