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Zbl 0956.70017
He, Jihuan
Homotopy perturbation technique. (English)
[J] Comput. Methods Appl. Mech. Eng. 178, No.3-4, 257-262 (1999). ISSN 0045-7825

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 2000:: *70K60 General perturbation schemes
70-08 Computational methods (mechanics of particles and systems)
34E10 Asymptotic perturbations (ODE)

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

Cited in: Zbl 1244.65104 Zbl 1222.35089 Zbl 1197.65101 Zbl 1197.65158 Zbl 1197.65141 Zbl 1192.65156 Zbl 1192.65137 Zbl 1192.65109 Zbl 1192.65102 Zbl 1192.65132 Zbl 1192.65091 Zbl 1168.65038 Zbl 1168.65370 Zbl 1165.82020 Zbl 1139.65085 Zbl 1138.76030 Zbl 1138.76029 Zbl 1120.65108 Zbl 1118.65394 Zbl 1191.34047

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