ABSTRACT
In this chapter, we present homotopy methods that are of fairly recent origin. These methods also provide us approximate analytical solutions that are in terms of series of functions of the independent variable. The functions in the solution constitute a set of base functions (which are linearly independent functions). These methods are applicable to problems modeled by linear as well as weakly/strongly nonlinear ordinary differential equations. The methods considered here are 1. The homotopy analysis method (HAM) initiated by Liao 2. The homotopy perturbation method (HPM) proposed by He 3. The optimal homotopy asymptotic method (OHAM) dis-
cussed by Marinca and Herisanu These methods and a number of offshoots have been extensively used recently to solve a wide variety of problems (see the Applications section at the end of the chapter).
