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In this article, an analytical solution procedure is described for solving two and three dimensional second order hyperbolic telegraph equation using a reliable semi-analytic method so called the reduced differential transform method (RDTM) subject to the appropriate initial condition. Using this method, it is possible to find an exact solution or a closed approximate solution of a differential equation. Various numerical examples are carried out to check the accuracy, efficiency, and convergence of the described method. The method is a powerful mathematical tool for solving a wide range of problems arising in engineering and sciences.

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.

In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.

This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

In this paper, an implicit exponential finite-difference scheme (Expo FDM) has been proposed for solving two dimensional nonlinear coupled viscous Burgers’ equations (VBEs) with appropriate initial and boundary conditions. The accuracy of the method has been illustrated by taking two numerical examples. Results are compared with exact solution and those already available in the literature by finding the L1, L2, L∞ and ER errors. Excellent numerical results indicate that the proposed scheme is efficient, reliable and robust technique for the numerical solutions of Burgers’ equation.

In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE). The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM). The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.