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Homotopy Analysis Method in Nonlinear Differential Equations || Relationship to Euler Transform

✍ Scribed by Liao, Shijun


Book ID
120238726
Publisher
Springer Berlin Heidelberg
Year
2012
Weight
910 KB
Category
Article
ISBN
3642251323

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Homotopy Analysis Method in Nonlinear Di
✍ Liao, Shijun πŸ“‚ Article πŸ“… 2012 πŸ› Springer Berlin Heidelberg 🌐 German βš– 804 KB

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM).Β  Unlike perturbation methods, the HAM has nothing to do with small/large phy

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A new transform, namely the homotopy transform, is defined for the first time. Then, it is proved that the famous Euler transform is only a special case of the so-called homotopy transform which depends upon one non-zero auxiliary parameter h and two convergent series P ΓΎ1 kΒΌ1 a 1;k ΒΌ 1 and In the

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In this paper, a one-step optimal approach is proposed to improve the computational efficiency of the homotopy analysis method (HAM) for nonlinear problems. A generalized homotopy equation is first expressed by means of a unknown embedding function in Taylor series, whose coefficient is then determi