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Numerical method for the solution of large systems of differential equations of the boundary layer typeA numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.
Document ID
19720025618
Acquisition Source
Legacy CDMS
Document Type
Other - NASA Technical Note (TN)
Authors
Green, M. J. (NASA Ames Research Center Moffett Field, CA, United States)
Nachtsheim, P. R. (NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
September 2, 2013
Publication Date
October 1, 1972
Subject Category
Fluid Mechanics
Report/Patent Number
A-4544
NASA-TN-D-7068
Accession Number
72N33268
Funding Number(s)
PROJECT: RTOP 186-68-51-01
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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