Application of Pade approximants to Wiener-Hopf factorization

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 65, Issue 3, 2000, Pages 257-281

  Abrahams, I David ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FOURIER TRANSFORMS; MATHEMATICAL MODELS;

PADE APPROXIMATION; WIENER-HOPF FACTORIZATION;

APPROXIMATION THEORY;

EID: 0034512738     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/65.3.257     Document Type: Article

References (28)

1. ABRAHAMS, I. D. 1996 Radiation and scattering of waves on an elastic half-space; a non-commutative matrix Wiener-Hopf problem. J. Mech. Phys. Solids 44, 2125-2154.
2. ABRAHAMS, I. D. 1997 On the solution of Wiener-Hopf problems involving noncommutative matrix kernel decompositions. SIAM J. Appl. Math. 57, 541-567.
3. ABRAHAMS, I. D. 1998 On the non-commutative factorization of Wiener-Hopf kernels of Khrapkov type. Proc. R. Soc. Land. A 454, 1719-1743.
4. ABRAHAMS, I. D. & DAVIS, A. M. J. 2000 Slow flow in a two dimensional duct with a semi-infinite splitter plate. SIAM. J. Appl. Math, to be submitted.
5. ABRAHAMS, I. D. & LAWRIE, J. B. 1995 On the factorization of a class of Wiener-Hopf kernels. IMA J. Appl. Math. 55, 35-47.
6. ABRAHAMS, I. D. & WICKHAM, G. R. 1991 The scattering of water waves by two semi-infinite opposed vertical walls. Wave Motion 14, 145-168.
7. ABRAHAMS, I. D. & WICKHAM, G. R. 1992 Scattering of elastic waves by a small inclined surface breaking crack. J. Mech. Phys. Solids 40, 1707-1733.
8. ATKINSON, C. 1977 Dynamic crack problems in dissimilar media. Mechanics of Fracture 4. (G. C. Sih ed). Noordhoff: Leyden, pp. 213-248.
9. BAKER, G. A. JR. 1975 Essentials of Padé Approximants. New York: Academic Press.
10. BAKER, G. A. JR. & GRAVES-MORRIS, P. 1996 Padé Approximants, 2nd edition, Cambridge: University Press.
11. CANNELL, P. A. 1976 Acoustic edge scattering by an elastic half-plane. Proc. R. Soc. Lond. A 350, 71-89.
12. CARLSON, J. F. & HEINS, A. E. 1947a The reflection of an electromagnetic plane wave by an infinite set of plates, I. Quart. Appl. Math. 4, 313-329.
13. CARLSON, J. F. & HEINS, A. E. 1947b The reflection of an electromagnetic plane wave by an infinite set of plates, II. Quart. Appl. Math. 5, 82-88.
14. CARRIER, G. F. 1959 Useful approximations in Wiener-Hopf problems. J. Appl. Phys. 30, 1769-1774.
15. CRIGHTON, D. G. 2000 Asymptotic factorization of Wiener-Hopf kernels. Wave Motion, forthcoming.
16. DAHL, P. H. & FRISK, G. V. 1991 Diffraction from the juncture of pressure release and locally reacting half-planes. J. Acoust. Soc. Am. 90, 1093-1100.
17. FREUND, L. B. 1993 Dynamic Fracture Mechanics. Cambridge: University Press.
18. HSIEH, W. W. & BUCHWALD, V. T. 1985 The scattering of a continental shelf wave by a long thin barrier lying parallel to the coast. J. Phys. Ocean. 15, 524-532.
19. JONES, C. M. A. 1990 Scattering by a semi-infinite sandwich panel perforated on one side. Proc. R. Soc. Lond. A 431, 465-479.
20. KELLER, J. B. 1953 A geometrical theory of diffraction. Institute of Mathematical Sciences. New York: University Press.
21. KHRAPKOV, A. A. 1971 Certain cases of the elastic equilibrium of an infinite wedge with a non-symmetric notch at the vertex, subjected to concentrated forces. Appl. Math. Mech. (PMM) 35, 625-637.
22. KOITER, W. T. 1954 Approximate solution of Wiener-Hopf type integral equations with applications, parts I-III. Koninkl. Ned. Akad. Wetenschap. Proc. B 57, 558-579.
23. KRANZER, H. C. & RADLOW, J. 1962 Asymptotic factorization for perturbed Wiener-Hopf problems. J. Math. Anal. Appl. 4, 240-256.
24. KRANZER, H. C. & RADLOW, J. 1965 An asymptotic method for solving perturbed Wiener-Hopf problems. J. Math. Mech. 14, 41-59.
25. LAWRIE, J. B. & ABRAHAMS, I. D. 1994 Acoustic radiation from two opposed semi-infinite coaxial cylindrical waveguides. II: separated ducts. Wave Motion 19,83-109.
26. NOBLE, B. 1988 Methods Based on the Wiener-Hopf Technique, 2nd edition, New York: Chelsea.
27. RAWLINS, A. D. 1975 The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane. Proc. R. Soc. Lond. A 346, 469-484.
28. ZHANG, B. & ABRAHAMS, I. D. 1995 The radiation of sound from a finite ring-forced cylindrical elastic shell. I: Wiener-Hopf analysis. Proc. R. Soc. Lond. A 450, 89-108.