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A coupling method of a homotopy technique and a perturbation technique for nonlinear problems. (English) Zbl 1068.74618
Summary: A coupling method of a homotopy technique and a perturbation technique is proposed to solve nonlinear problems. In contrast to the traditional perturbation methods, the proposed method does not require a small parameter in the equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter $$p\in[0,1]$$ is constructed, and the imbedding parameter is considered as a ”small parameter”. So the proposed method can take full advantage of the traditional perturbation methods. Some examples are given. The results reveal that the new method is very effective and simple.

##### MSC:
 74S30 Other numerical methods in solid mechanics (MSC2010) 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
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