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On the homotopy analysis method for nonlinear problems. (English) Zbl 1086.35005
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:
35A25Other special methods (PDE)
76M25Other numerical methods (fluid mechanics)
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)