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Homotopy analysis method: A new analytical technique for nonlinear problems. (English) Zbl 0927.65069
Summary: The basic ideas of a new kind of analytical technique, namely the homotopy analysis method (HAM), are simply described. Different from perturbation techniques, the HAM does not depend on whether or not there exist small parameters in the nonlinear equations under consideration. Therefore, it provides us with a powerful tool to analyse strongly nonlinear problems. A simple but typical example is used to illustrate the validity and the great potential of the HAM. Moreover, a pure mathematical theorem, namely the general Taylor theorem, is given in appendix, which provides us with some rational knowledge for the validity of this new analytical technique.
MSC:
65H20Global numerical methods for nonlinear algebraic equations, including homotopy approaches