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Use of Hybrid Functions in the Method of Collocation

Published online by Cambridge University Press:  28 July 2016

Bertram Kelin*
Affiliation:
Los Angeles, California

Extract

As pointed out in previous work, in the method of collocation the functions used usually need not be orthogonal or integrable in closed form. Therefore function of different types may be mixed together in representing unknown quantities. Such function may be aptly called hybrid functions. Also, it has been found that usually it is better to represent unknown quantities by similarly looking functions instead of by a series involving higher harmonics. The idea is that by using similar looking functions it is possible to avoid poor regions for collocation, such as near nodal points, and so on, and closer fit in certain regions is assured. Thus if one knows approximately what the function sought looks like, one should try to find a set of function all of which resemble this desired shape, instead of taking an arbitrary set of harmonics when using the method of collocation. Simple examples below illustrate this approach and indicate the good results that can be expected in general.

Type
Technical Notes
Copyright
Copyright © Royal Aeronautical Society 1955

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References

1. Klein, B. and Cox, H. L. (1954). Approximate Structural Analysis by the Method of Collocation. Journal of the Aeronautical Sciences, Vol. 21, No. 10, p. 719, October 1954.Google Scholar
2. Timoshenko, S. and Goodier, J. N. (1951). Theory of Elasticity. McGraw–Hill Book Company, New York, 1951.Google Scholar
3. Wang, Chi–teh (1953). Applied Elasticity. McGraw–Hill Book Company, New York, 1953.Google Scholar