Homotopy Analysis Method for the Coupled System of Nonlinear Partial Differential Equations

The homotopy analysis method (HAM) is implemented to obtain the approximate solutions of the nonlinear system of one dimensional thermo-elasticity. The results obtained ensure that this method is capable of solving a large number of nonlinear differential equations that have wide applications in physics and engineering. This analytic technique is valid for dealing with the nonlinearity and provides a convenient way of controlling the convergence region and rate of the series solution. The results obtained by the present method are compared with exact solutions, and it is seen that they are in excellent agreement. Computations are performed using the symbolic computational package MATHEMATICA. This work verifies the validity and the potential of the HAM for the study of nonlinear system.