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Approximation to transients by means of Laguerre series

Published online by Cambridge University Press:  24 October 2008

J. W. Head
J. W. Head
Affiliation:
Research DepartmentB.B.C. Engineering Division
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Abstract

Ward(1) has discussed a method, introduced by Tricomi (6), of calculating transients by means of series involving Laguerre functions which in some cases makes it unnecessary to determine poles of the relevant characteristic function. This method is here investigated with special reference to conditions for convergence and adjustments for improving convergence; some of the examples discussed by Ward are reconsidered.

Both in Ward's paper and here the location of poles of the characteristic function is assumed to be approximately known. In some cases the determination of poles of outstandingly small or large modulus and their separation from the remainder may be the most satisfactory procedure. Lin's method (2) for determining a quadratic factor of a polynomial is more widely applicable than has previously been supposed, and this is discussed in bare outline, without proof, here, but in detail, with adequate numerical examples, elsewhere (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 4 , October 1956 , pp. 640 - 651
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Ward, E. E.The calculation of transients in dynamical systems. Proc. Camb. Phil. Soc. 50 (1954), 49–59.CrossRefGoogle Scholar
(2)Morris, J. and Head, J. W.Note on Lin's iteration process for the extraction of complex roots of algebraic equations. Quart. J. Mech. 6 (1953), 391–7.CrossRefGoogle Scholar
(3)Head, J. W.Widening the applicability of Lin's iteration process for determining quadratic factors of polynomials. To be published in Quart. J. Mech.Google Scholar
(4)Morris, J. and Head, J. W.Polynomial characteristic equations. Aircr. Engng, 27 (1955), 419–20.CrossRefGoogle Scholar
(5)Olver, F. J. W.The evaluation of zeros of high-degree polynomials. Phil. Trans. A, 244 (1952), 385–415.Google Scholar
(6)Tricomi, F.Trasformazione di Laplace e polinomi di Laguerre. I. R. C. Accad. Lincei (6), 21 (1935), 235.Google Scholar