NUMERICALLY SOLVING STRONGLY NONLINEAR PROBLEMS BY MEANS OF NO ITERATIONS

Based on the Homotopy Analysis Method which is a new kind of nonlinear analytic technique proposed in references2]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 formulas which contain the traditional approaches.

NUMERICALLY SOLVING STRONGLY NONLINEAR PROBLEMS BY MEANS OF NO ITERATIONS

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 formulas which contain the traditional approaches.