AVOID THE UNCONTROLLABILITY PROBLEMS OF THE NONZERO ENDPOINT CONDITIONS VIA HOMOTOPY ANALYSIS METHOD

In this paper, the homotopy analysis method (HAM) and Taylor series are presented and applied to nonlinear non-homogenous of higher-order initial value problems (IVPs). A comparative study between the new technique of the HAM (NHAM) and the HAM is conducted. The main advantage of NHAM is that one can avoid the uncontrollability problems of the nonzero endpoint conditions encountered in the traditional HAM. Several illustrative examples are given to demonstrate the effectiveness and reliability of NHAM