Direct solutions of nth-order IVPs by homotopy-perturbation method

Abstract

In this paper, a class of linear and nonlinear nth-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by the homotopy-perturbation method (HPM). The HPM can be considered as one of the new methods belonging to the general classification of perturbation methods. Generally, the HPM deals with exact solvers for linear differential equations and approximative solvers for nonlinear equations. Several test cases are chosen to demonstrate the efficiency of HPM.

Keywords:

• homotopy-perturbation method
• initial value problems
• series solution

2000 AMS Subject Classification :

• 64-XX
• 34-XX

Acknowledgements

The authors acknowledge the financial supports received from the Academy of Sciences, Malaysia via the SAGA Grant No. P24c (STGL-011-2006), the Malaysian Technical Cooperation Program and the International Islamic University Chittagong, Bangladesh.