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The Stokes phenomenon and certain nth-order differential equations

III. Matrix applications

Published online by Cambridge University Press:  24 October 2008

J. Heading
J. Heading
Affiliation:
The University of SouthamptonSouthampton
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Extract

In papers I(1) and II(2), the author has investigated the Stokes phenomenon associated with the arbitrary constants that occur in the asymptotic expressions of solutions of the nth-order differential equation

and has provided rules for tracing a given linear combination of n such asymptotic expressions across certain defined lines, designated as Stokes lines, anti-Stokes lines and branch-cuts. The object of these investigations is to apply the results to the approximate solution of more complicated linear differential equations of the nth order, and to this end it is an advantage to develop the theory using matrix techniques. In the present paper, the equations are recast into a special matrix form, and it is shown how the results obtained in II may be used in a systematic manner.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 4 , October 1960 , pp. 329 - 341
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Heading, J.Proc. Camb. Phil. Soc. 53 (1957), 399.CrossRefGoogle Scholar
(2)Heading, J.Proc. Camb. Phil. Soc. 53 (1957), 419.CrossRefGoogle Scholar
(3)Clemmow, P. C. and Heading, J.Proc. Camb. Phil. Soc. 50 (1954), 319.CrossRefGoogle Scholar