ON THE EQUIVALENCE OF THE SOLUTIONS OF NONLINEAR PROBLEMS BY THE HE VARIATIONAL ITERATION METHOD AND THE TEMIMI–ANSARI METHOD: TRANSFER PHENOMENA

Approximate solutions of a number of nonlinear problems (heat-transfer, reaction diffusion, thin-film boiling) have been obtained using the Temimi–Ansari method and the He variational iteration method. The solutions of such problems by the indicated methods were found to be identical, and, in the case of small iterations, they did not provide a useful approximation either in the sense of convergent series or in the sense of asymptotic ones. It was shown that the obtaining of the indicated solutions with the use of a large number of iterations is practically impossible because of the extreme cumbersomeness of the computational procedure. Nevertheless, the Temimi– Ansari method offers an important advantage over the He method in that it does not involve the search for an optimum Lagrange multiplier and, at the same time, provides a simple iteration scheme of obtaining a system of recursion linear equations solved fairly easily.

Author:  V. A. Kot
Keywords:  nonlinear differential equations, nonlinear problems, approximate solution, iterative method, thermophysical problems, heat transfer, reaction diffusion, thin-film boiling
Page:  889