Direct Solution of nth‐Order IVPs by Homotopy Analysis Method

Direct solution of a class of nth‐order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven‐ and eight‐order Runge‐Kutta method (RK78).