An explicit, totally analytic approximate solution for Blasius' viscous flow problems

By means of using an operator A to denote non-linear differential equations in general, we first give a systematic description of a new kind of analyt ic technique for non-linear problems, namely the homotopy analysis method ( HAM). Secondly, we generally discuss the convergence of the related approxi mate solution sequences and show that, as long as the approximate solution sequence given by the HAM is convergent, it must converge to one solution o f the non-linear problem under consideration. Besides, we illustrate that e ven though a non-linear problem has one and only one solution, the sole sol ution might have an infinite number of expressions. Finally, to show the va lidity of the HAM, we apply it to give an explicit, purely analytic solutio n of the 2D laminar viscous flow over a semi-infinite flat plate. This expl icit analytic solution is valid in the whole region eta = [0, +infinity) an d can give, the first time in history (to our knowledge), an analytic value f " (0) = 0.33206, which agrees very well with Howarth's numerical result. This verifies the validity and great potential of the proposed homotopy an alysis method as a new kind of powerful analytic tool. (C) 1999 Elsevier Sc ience Ltd. All rights reserved.