Homotopy perturbation technique. (English) Zbl 0956.70017

He, Jihuan

Comput. Methods Appl. Mech. Eng. 178, No. 3-4, 257-262 (1999).

Summary: The homotopy perturbation technique does not depend upon a small parameter in the equation. By the homotopy technique in topology, a homotopy can be constructed with an imbedding parameter \(p\in [0,1]\), which is considered as a “small parameter”. Here we give some examples, and demonstrate that the approximations obtained by the proposed method are uniformly vaild not only for small parameters, but also for very large parameters.

MSC:

70K60	General perturbation schemes for nonlinear problems in mechanics
34A45	Theoretical approximation of solutions to ordinary differential equations
34E10	Perturbations, asymptotics of solutions to ordinary differential equations

Keywords:

large parameter; Lighthill equation; Poincaré-Lighthill-Kuo method; Duffing equation; homotopy perturbation technique; imbedding parameter

References:

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