Abstract
In this entry, we describe the basic ideas of the homotopy analysis method (HAM), an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers. HAM fundamentally overcomes the excessive dependence on small parameters in the framework of perturbation theory, and its validity has nothing to do with small/large physical parameter of the studied nonlinear problem. So, it has a wide range of applications. In addition, HAM provides us great freedom to choose the base function, so that a better base function can be selected to approximate the solution of the problem more effectively. Furthermore, unlike all other analytical approximation methods, we can guarantee the convergence of solution series in a simple way in the framework of HAM. In general, HAM provides a new way of thinking that how to get the analytical approximate solution for nonlinear problems and opens up a new way for solving nonlinear problems (especially strong nonlinear problems without small parameters).
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Yang, X., Lin, Z. (2020). Homotopy Analysis Method. In: Cui, W., Fu, S., Hu, Z. (eds) Encyclopedia of Ocean Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-6963-5_271-1
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DOI: https://doi.org/10.1007/978-981-10-6963-5_271-1
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