Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-18T07:39:09.150Z Has data issue: false hasContentIssue false

High frequency solutions of the delta wing equations*

Published online by Cambridge University Press:  14 November 2011

B. A. Hargrave
Affiliation:
Department of Mathematics, The University, Aberdeen†

Synopsis

Uniformly valid asymptotic approximations are presented for solutions of the angular equations associated with the problem of diffraction by a plane angular sector. Error estimates are provided for all approximations. The asymptotic variable is related to the number of zeros of the solutions of the angular equations and expressions for the eigenvalues of the equations are presented in decoupled form.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Hargrave, B. A.Numerical approximation of the eigenvalues of Sturm-Liouville systems. J. Computational Phys. 20 (1976).CrossRefGoogle Scholar
2Hargrave, B. A. and Sleeman, B. D.The numerical solution of two-parameter eigenvalue problems in ordinary differential equations with an application to the problem of diffraction by a plane angular sector. J. Inst. Math. Appl. 14 (1974), 922.CrossRefGoogle Scholar
3Hargrave, B. A. and Sleeman, B. D.Lamé polynomials of large order. SIAM J. Math. Anal. 8 (1977), 800842.CrossRefGoogle Scholar
4Krauss, L. and Levine, L. M.Diffraction by an elliptic cone. Comm. Pure Appl. Math. 14 (1961), 4968.CrossRefGoogle Scholar
5Olver, F. W. J.Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders. J. Res. Nat. Bur. Standards Sect. B 63 (1959), 131169.CrossRefGoogle Scholar
6Olver, F. W. J.Asymptotics and Special Functions (New York: Academic Press, 1974).Google Scholar
7Olver, F. W. J.Second-order linear differential equations with two turning points. Phil. Trans. Roy. Soc. London Ser. A. 278 (1975), 137174.Google Scholar
8Olver, F. W. J.Improved error bounds for second-order differential equations with two turning points. J. Res. Nat. Bur. Standards Sect. B. 80 (1976), 437440.CrossRefGoogle Scholar
9Sack, R. A.Variational solutions for eigenvalues of single and coupled Lamé equations. J. Inst. Math. Appl. 10 (1972), 279288.CrossRefGoogle Scholar
10Taylor, R. S.A new approach to the delta wing problem. J. Inst. Math. Appl. 7 (1971), 337347.CrossRefGoogle Scholar