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Homotopy-perturbation method for pure nonlinear differential equation. (English) Zbl 1142.65418
Summary: In this paper, the homotopy-perturbation method proposed by J.-H. He is adopted for solving pure strong nonlinear second-order differential equation. For the oscillatory differential equation the initial approximate solution is assumed in the form of Jacobi elliptic function and the forementioned method is used for obtaining of the approximate analytic solution. Two types of differential equations are considered: with strong cubic and strong quadratic nonlinearity. The obtained solution is compared with exact numerical one. The difference between these solutions is negligible for a long time period. The method is found to work extremely well in the examples, but the theoretical reasons are not yet clear.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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