Dirichlet series solution of equations arising in boundary-layer theory. (English) Zbl 0993.76066
Summary: We consider the differential equation \(F'''+ AFF''+ BF^{\prime 2}= 0\), where \(A\) and \(B\) are arbitrary constants, subject to different boundary conditions. This class of equations occurs in boundary-layer theory. The proposed Dirichlet series method, in conjunction with a unconstrained optimization procedure, is found to be useful in analyzing these problems. The series so generated is analyzed using Euler transformation and Padé approximants.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |
Keywords:
analytic continuation; Falkner-Skan equation; boundary-layer theory; Dirichlet series method; unconstrained optimization; Euler transformation; Padé approximantsReferences:
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