Padé approximants and Adomian decomposition method for solving the Flierl-Petviashivili equation and its variants. (English) Zbl 1107.65061
Summary: We present a reliable combination of Adomian decomposition algorithm and Padé approximants to investigate the Flierl-Petviashivili (FP) equation and its variants. The approach introduces an alternative framework designed to overcome the difficulty of the singular point at \(x = 0\). We also investigate two generalized variants of the FP equation. The proposed framework reveals quite a number of remarkable features of the combination of the two algorithms.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
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