Approximate analytical and numerical solutions of a nonlinear boundary value problem in fluid mechanics based on symmetry reduction

Abstract

This work presents applications of the L i e symmetry method to a boundary value problem (BVP) of the governing equations in fluid mechanics. The Wu differential characteristic set algorithm is used to obtain a group of multi-parameter symmetries for the BVP, and the L i e symmetry method is adopted to simplify the BVP into some initial value problems of reduced diffusion equations. Approximate analytical and numerical solutions are then obtained by utilizing the homotopy perturbation method and the Runge–Kutta method respectively, and compared to exhibit the convergence of approximate analytical solutions. The formulation developed here could be applied to studies of other nonlinear BVPs in fluid mechanics.