Stability of power-law discs - I. The Fredholm integral equation

Monthly Notices of the Royal Astronomical Society

Volumn 300, Issue 1, 1998, Pages 83-105

  Evans, N W ^a   Read, J C A ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Celestial mechanics, stellar dynamics; Galaxies: kinematics and dynamics; Galaxies: spiral; Instabilities; Methods: analytical; Methods: numerical

Indexed keywords

ANGULAR DISTRIBUTION; ASTROPHYSICS; BOLTZMANN EQUATION; GALAXIES; NUMERICAL METHODS; STARS;

CELESTIAL MECHANIC, STELLAR DYNAMIC; CELESTIAL MECHANICS; FREDHOLM'S INTEGRAL EQUATION; GALAXIES: KINEMATICS AND DYNAMICS; GALAXIES: SPIRALS; METHOD: NUMERICAL; METHODS:ANALYTICAL; NORMAL MODES; POWER-LAW; STELLAR DYNAMICS;

INTEGRAL EQUATIONS;

EID: 0039274595     PISSN: 00358711     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-8711.1998.01863.x     Document Type: Article

References (34)

1. Abramowitz M., Stegun I. A., 1965, Handbook of Mathematical Functions. Dover, New York
2. Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton Univ. Press, Princeton, NJ
3. Bisnovatyi-Kogan E., 1976, Sov. Astron. Lett., 1, 177
4. Casertano S., van Gorkom J. H., 1991, AJ, 101, 1231
5. Courant R., Hilbert D., 1953, Methods of Mathematical Physics. Interscience, New York
6. Delves L. M., Mohamed J. L., 1985, Computational Methods for Integral Equations. Cambridge Univ. Press, Cambridge
7. Earn D. J. D., 1993. PhD thesis, Cambridge University
8. Earn D. J. D., Sellwood J. A., 1995, ApJ, 451, 533
9. Evans N. W., 1994, MNRAS, 267, 333
10. Evans N. W., Collett J. L., 1993, MNRAS, 264, 353
11. Jeans J. H., 1919, Problems of Cosmogony & Stellar Dynamics. Cambridge Univ. Press, Cambridge
12. Kalnajs A. J., 1965, PhD thesis, Harvard University
13. Kalnajs A. J., 1971, ApJ, 166, 275
14. Kalnajs A. J., 1972, ApJ, 175, 63
15. Lemos J. P. S., Kalnajs A. J., Lynden-Bell D., 1991, ApJ, 375, 484
16. Lynden-Bell D., Ostriker J. P., 1967, MNRAS, 136, 101
17. Merritt D., Sellwood J. A., 1994, ApJ, 425, 551
18. Mestel L., 1963, MNRAS, 126, 553
19. Mihalas D., Binney J. J., 1987, Galactic Astronomy. W. H. Freeman, San Francisco
20. Ostriker J. P., Peebles P. J E., 1973, ApJ, 186, 467
21. Palmer P. L., Papaloizou J., 1990, MNRAS, 243, 263
22. Press W., Flannery B., Teukolsky S., Vetterling W., 1989, Numerical recipes: the art of scientific computing. Cambridge Univ. Press, Cambridge
23. Prudnikov A. P., Brychkov Y. A., Mavichev O., 1986, Integrals and Series, Vol. 1. Gordon and Breach, New York
24. Ralston A., Rabinowitz P., 1978, A First Course in Numerical Analysis. McGraw-Hill, New York
25. Read J. C. A., 1997, PhD thesis, Oxford University
26. Rubin V. C., Ford W. K., Thonnard N., 1978, ApJ, 225, L107
27. Schmitz F., Ebert R., 1987, A&A, 181, 41
28. Sellwood J. A., Athanassoula E., 1986, MNRAS, 221, 195
29. Smith B. T., Boyle J. M., Dongarra J. J., Garbow B. S., Ikebe Y., Klema V. C., Moler C. B., 1972, Lecture Notes in Computer Science, Vol. 6, 2nd edn. Springer-Verlag, Berlin
30. Snow C., 1952, Hypergeometric and Legendre Functions with Applications to the Integral Equations of Potential Theory. National Bureau of Standards, Washington
31. Toomre A., 1977, ARA&A, 15, 437
32. Toomre A., 1981, in Fall S. M., Lynden-Bell D., eds, The Structure and Evolution of Normal Galaxies. Cambridge Univ. Press, Cambridge, p. 111
33. Tricomi F., 1985, Integral Equations. Dover, New York
34. Zang T. A., 1976, PhD thesis, Massachusetts Institute of Technology