The compound matrix method for multi-point boundary-value problems

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 77, Issue 10, 1997, Pages 767-776

  Ivansson, S ^a  

^a SWEDISH DEFENCE RESEARCH AGENCY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944456020     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19970771009     Document Type: Article

References (37)

1. AITKEN, A. C.: Determinants and matrices. Oliver and Boyd, Edinburgh 1956.
2. AKI, K.; RICHARDS, P.: Quantitative seismology. Freeman, San Francisco 1980.
3. ASCHER, U.; MATTHEIJ, R.; RUSSELL, R.: Numerical solution of boundary value problems for ordinary differential equations. Prentice-Hall, New Jersey 1988.
4. CHEN, X.: A systematic and efficient method of computing normal modes for multilayered half-space. Geophys. J. Int. 115 (1993), 391-409.
5. COPPEL, W. A.: Dichotomies in stability theory. Springer Lecture Notes in Mathematics 629, New York 1978.
6. CORMIER, V. F.; MANDAL, B.; HARVEY, D.: Incorporation of velocity gradients in the synthesis of complete seismograms by the locked mode method. Bull. Seism. Soc. Amer. 81 (1991), 897-930.
7. CONTE, S. D.: The numerical solution of linear boundary value problems. SIAM Review 8 (1966), 309-321.
8. DE HOOG, F. R.; MATTHEIJ, R. M. M.: On dichotomy and well conditioning in BVP. SIAM J. Numer. Anal. 24 (1987), 89-105.
9. DICKSON, L. E.: First course in the theory of equations. Wiley, London 1922.
10. DIECI, L.; OSBORNE, M. R.; RUSSELL, R. D.: A Riccati transformation method for solving linear BVPs. I, II. SIAM J. Numer. Anal. 25 (1988), 1055-1092.
11. EVANS, R. B.: The decoupling of seismic waves. Wave Motion 8 (1986), 321-328.
12. GANTMACHER, F. R.: The theory of matrices. Chelsea Publ., New York 1960.
13. GILBERT, F.; BACKUS, G.: Propagator matrices in elastic wave and vibration problems. Geophysics 31 (1966), 326-332.
14. GODUNOV, S.: On the numerical solution of boundary value problems for systems of lineary ordinary differential equations. Uspehi Mat. Nauk 16 (1961), 171-174.
15. GOODMAN, T. R.; LANCE, G. N.: The numerical solution of two-point boundary value problems. Math. Tables Aid. Comput. 10 (1956), 82-86.
16. HARVEY, D. J.: Seismogram synthesis using normal mode superposition: the locked mode approximation. Bull. Seism. Soc. Amer. 66 (1981), 37-69.
17. IVANSSON, S.: Delta-matrix factorization for fast propagation through solid layers in a fluid-solid medium. J. Comput. Phys. 108 (1993), 357-367.
18. IVANSSON, S.: Seismo-acoustic wave fields: Compound-matrix methods for range-independent fluid-solid media. PhD Thesis. Royal Institute of Technology, Stockholm 1994.
19. JENSEN, F.; KUPERMAN, W.; PORTER, M.; SCHMIDT, H.: Computational ocean acoustics. AIP Press, New York 1994.
20. KARASALO, I.: Exact finite elements for wave propagation in range-independent fluid-solid media. J. Sound Vibrat. 172 (1994), 671-688.
21. KELLER, H.: Numerical solution of two-point boundary value problems. SIAM, Soc. for Industrial and Applied Math., Philadelphia 1976.
22. KIND, R.: Computation of reflection coefficients for layered media. J. Geophys. 42 (1976), 373-380.
23. KIND, R.: The reflectivity method for a buried source. J. Geophys. 44 (1978), 603-612.
24. LENTINI, M.; OSBORNE, M.; RUSSELL, R.: The close relationships between methods for solving two-point boundary value problems. SIAM J. Numer. Anal. 22 (1985), 280-309.
25. NG, B. S.; REID, W. H.: An initial value method for eigenvalue problems using compound matrices. J. Computat. Phys. 30 (1979), 125-136.
26. NG, B. S.; REID, W. H.: A numerical method for linear two-point boundary-value problems using compound matrices. J. Computat. Phys. 33 (1979), 70-85.
27. NG, B. S.; REID, W. H.: The compound matrix method for ordinary differential systems. J. Computat. Phys. 58 (1985), 209-228.
28. PESTEL, E.; LECKIE, F.: Matrix methods in elastomechanics. McGraw-Hill, New York 1963.
29. PORTER, M. B.; REISS, E. L.: A numerical method for bottom interacting ocean acoustic normal modes. J. Acoust. Soc. Amer. 77 (1985), 1760-1767.
30. ROBERTS, S.; SHIPMAN, J.: Two-point boundary value problems: shooting methods. Elsevier, New York 1972.
31. SCHMIDT, H.: SAFARI, Seismo-Acoustic Fast field Algorithm for Range-Independent environments. SACLANTCEN Report Sr-113, 1988.
32. SCHWAB, F.; NAKANISHI, K.; CUSCITO, M.; PANZA, G. F.; LIANG, G.; FREZ, J.: Surface-wave computations and the synthesis of theoretical seismograms at high frequencies. Bull. Seism. Soc. Amer. 74 (1984), 1555-1578.
33. SCOTT, M.; WATTS, H.: Computational solution of linear two-point boundary value problems via orthonormalization. SIAM J. Numer. Anal. 14 (1977), 40-70.
34. WATSON, T. H.: A note on fast computation of Rayleigh wave dispersion in the multi-layered half-space. Bull. Seism. Soc. Amer. 60 (1970), 161-166.
35. WHYBURN, W. M.: Differential equations with general boundary conditions. Bull. Amer. Math. Soc. 48 (1942), 692-704.
36. WHYBURN, W. M.: Differential systems with general boundary conditions. Univ. Calif. Publ. Math. 2 (1944), 45-61.
37. WOODHOUSE, J. H.: The calculation of eigenfrequencies and eigenfunctions of the free oscillations of the Earth and the Sun. In: DOORNBOS, D. (ed.): Seismological algorithms: computational methods and computer programs. Academic Press, 1988, pp. 321-370.