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A dynamical model of HIV infection of CD4+ T cells is solved numerically using an approximate analytical method so-called the differential transform method (DTM). The solution obtained by the method is an infinite power series for appropriate initial condition, without any discretization, transformation, perturbation, or restrictive conditions. A comparative study between the present method, the classical Euler’s and Runge–Kutta fourth order (RK4) methods is also carried out.

In this article, we present homotopy perturbation method, adomian decomposition method and differential transform method to obtain a closed form solution of the (1 + n)-dimensional Burgers’ equation. These methods consider the use of the initial or boundary conditions and find the solution without any discritization, transformation, or restrictive conditions and avoid the round-off errors. Four numerical examples are provided to validate the reliability and efficiency of the three methods.