Approximate explicit solutions of Orr–Sommerfeld equations and heat transfer in a geometry with variable cross section by He’s methods and comparison with the ADM and DTM

Abstract

In this paper two examples are studied; the Orr–Sommerfeld and nonlinear heat transfer equation. He’s variational iteration method (VIM) and Adomian’s decomposition method (ADM) are applied to the Orr–Sommerfeld equation. He’s VIM and differential transformation method (DTM) are applied to the nonlinear heat transfer equation. Comparison of different methods represents while the effect of the nonlinear term in the heat transfer equation is negligible, VIM and DTM lead approximately to the same answers; and when the kinematic viscosity in the Orr–Sommerfeld equation is small, VIM and ADM lead nearly to the same results.