Article

# Direct Solution of nth-Order IVPs by Homotopy Analysis Method

Differential Equations and Nonlinear Mechanics 01/2009;
Source: DOAJ

ABSTRACT 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).

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### Keywords

approximate analytical solutions

auxiliary parameter

comparable accuracy

Direct solution

HAM solutions

homotopy analysis method

nth-order initial value problems

series solutions

seven-