Numerically solving strongly nonlinear pro- blems by means of no iterations

摘要

Based on the Homotopy Analysis Method which is a new kind of nonlinear analytic technique proposed in references[2][3][4]. A direct numerical technique for strongly non-linear problems is proposed in general. Then an example in fluid mechanics, say, the 2D laminar viscous flow over semi-infinite plate, is used to illustrate its validity and great potential. Different from nearly all traditional numerical methods for nonlinear problems, this approach can give accurate enough approximations of a strongly nonlinear problem even by means of no iterations. Moreover, it can provide a family of iterative for- mulas which contain the traditional approaches.