In this paper, we present a reliable combination of homotopy perturbation method and Padé approximants to investigate the Flierl-Petviashivili (FP) equation. The approach introduces a new transformation necessary for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed homotopy perturbation method is applied to the reformulated first order initial value problem which leads the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm may be considered as an efficient and reliable scheme for solving Flierl- Petviashivili equation and other singular boundary value problems.
Mohynd-Din, Syed T. and Noor, Muhammad A.
Homotopy Perturbation Method and Padé Approximants for Solving Flierl-Petviashivili Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 3,
2, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol3/iss2/6