On the homotopy analysis method for nonlinear problems. (English) Zbl 1086.35005

Liao, Shijun

Appl. Math. Comput. 147, No. 2, 499-513 (2004).

Summary: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e., the algebraically decaying viscous boundary layer flow due to a moving sheet. Two rules, the rule of solution expression and the rule of coefficient ergodicity, are proposed, which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering. An explicit analytic solution is given for the first time, with recursive formulas for coefficients. This analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem.

MSC:

35A25	Other special methods applied to PDEs
76M25	Other numerical methods (fluid mechanics) (MSC2010)
76D10	Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

Homotopy analysis method; Analytic; Nonlinear; Similar boundary-layer; Stretching wall

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