A Boundary-layer Flow with an Infinite Number of Solutions

Abstract

In this chapter, the Mathematica package BVPh (version 1.0) based on the homotopy analysis method (HAM) is used to gain exponentially and algebraically decaying solutions of a nonlinear boundary-value equation in an infinite interval. Especially, an infinite number of algebraically decaying solutions were found for the first time by means of the HAM, which illustrate the originality and validity of the HAM for nonlinear boundary-value problems. 10.1 Introduction In this chapter, we illustrate the validity of the Mathematica package BVPh (version 1.0) for nonlinear boundary-value problems in an infinite interval, governed by a nth-order nonlinear ordinary differential equation (ODE) F [z [ [ , u] = 0, 0 z