Some Methods Based on the HAM
In this chapter, some analytic and semi-analytic techniques based on the homotopy analysis method (HAM) are briefly described, including the so-called “homotopy perturbation method”, the optimal homotopy asymptotic method, the spectral homotopy analysis method, the generalized boundary element method, and the generalized scaled boundary finite element method. The relationships between these methods with the HAM are also revealed.
KeywordsBoundary Element Method Perturbation Method Homotopy Analysis Method Homotopy Perturbation Method Deformation Equation
Unable to display preview. Download preview PDF.
- Karmishin, A.V., Zhukov, A.T., Kolosov, V.G.: Methods of Dynamics Calculation and Testing for Thin-walled Structures (in Russian). Mashinostroyenie, Moscow (1990).Google Scholar
- Liao, S.J.: The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems. PhD dissertation, Shanghai Jiao Tong University (1992).Google Scholar
- Lyapunov, A.M.: General Problem on Stability of Motion (English translation). Taylor & Francis, London (1992).Google Scholar
- Wolf, J.P.: The scaled boundary finite-element method. Wiley, Chichester (2003).Google Scholar