Approximate time dependent solutions of partial differential equations: The MaxEnt-Minimum Norm approach

Physica A: Statistical Mechanics and its Applications

Volumn 265, Issue 1-2, 1999, Pages 224-234

  Malaza, E D ^a   Miller, H G ^b   Plastino, A R ^b,d   Solms, F ^c  

^a UNIVERSITY OF LIMPOPO   (South Africa)

^b UNIVERSITY OF PRETORIA   (South Africa)

^c UNIVERSITY OF JOHANNESBURG   (South Africa)

^d UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; EQUATIONS OF MOTION; INVERSE PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING;

TSALLIS NONEXTENSIVE THERMOSTATISTICS;

STATISTICAL MECHANICS;

EID: 0033098344     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00482-8     Document Type: Article

References (46)

1. A.I. Khinchin, Mathematical Foundations of Information Theory, Dover, New York, 1957.
2. E.T. Jaynes, Phys. Rev. 106 (1957) 620.
3. E.T. Jaynes, Phys. Rev. 108 (1957) 171.
4. E.T. Jaynes in: W.K. Ford (Ed.), Statistical Physics, Benjamin, New York, 1963.
5. A. Katz, Statistical Mechanics, Freeman, San Francisco, 1967.
6. A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, London, 1971.
7. R. Balian, From Microphysics to Macrophysics, Springer, Berlin, 1992.
8. W. Grandy, Foundations of Statistical Mechanics, Reidel, Dordrecht, 1987.
9. H. Grabert, Projection Operator Techniques in Nonequilibrium Statistical Mechanics, Springer, Berlin, 1982.
10. A.R. Plastino, A. Plastino, Physica A 232 (1996) 458.
11. P. Hick, G. Stevens, Astron. Astrophys. 172 (1987) 350.
12. J. Baker-Jarvis, M. Racine, J. Alameddine, J. Math. Phys. 30 (1989) 1459.
13. J. Baker-Jarvis, J. Math. Phys. 30 (1989) 302.
14. J. Baker-Jarvis, J. Alameddine, D. Schultz, Numer. Meth. Partial Differential Equations 5 (2) (1989) 133-142.
15. Y. Alhassid, R. Levine, J. Chem. Phys. 67 (1977) 4321.
16. Y. Alhassid, R. Levine, Phys. Rev. A 18 (1978) 89.
17. D. Otero, A. Plastino, A.N. Proto, G. Zannoli, Phys. Rev. A 26 (1982) 1209.
18. D. Otero, A. Plastino, A.N. Proto, G. Zannoli, Z. Phys. Rev. A 316 (1984) 323.
19. N.Z. Tishby, R.D. Levine, Phys. Rev. A 30 (1984) 1427.
20. E. Duering, D. Otero, A. Plastino, A.N. Proto, Phys. Rev. A 32 (1985) 2455.
21. R. Levine, D. Otero, A. Plastino, A.N. Proto, Nucl. Phys. A 454 (1986) 338.
22. D. Otero, A. Plastino, A.N. Proto, S. Misrahi, Phys. Rev. A 33 (1986) 3446.
23. E. Duering, D. Otero, A. Plastino, A.N. Proto, Phys. Rev. A 35 (1987) 2314.
24. R. Balian, M. Veneroni, Ann. Phys. 164 (1985) 334.
25. R. Balian, M. Veneroni, Ann. Phys. 174 (1987) 229.
26. R. Balian, M. Veneroni, Ann. Phys. 187 (1988) 29.
27. J. Aliaga, D. Otero, A. Plastino, A.N. Proto, Phys. Rev. A 37 (1988) 918.
28. C. Tsallis, Physica A 221 (1995) 277; Fractals 6 (1995) 539, and references therein.
29. C. Tsallis, Physica A 221 (1995) 277; Fractals 6 (1995) 539, and references therein.
30. C. Tsallis, J. Stat. Phys. 52 (1988) 479.
31. E.M.F. Curado, C. Tsallis, J. Phys. A 24 (1991) L69; Corrigenda: 24 (1991) 3187; 25 (1992) 1019.
32. A.R. Plastino, A. Plastino, Phys. Lett. A 177 (1993) 177.
33. A.R. Plastino, C. Anteneodo, Ann. Phys. 255 (1997) 250.
34. G.A. Raggio, J. Math. Phys. 36 (1995) 4785.
35. G.R. Guerberoff, G.A. Raggio, J. Math. Phys. 37 (1996) 1776.
36. G.R. Guerberoff, P.A. Pury, G.A. Raggio, J. Math. Phys. 37 (1996) 1790.
37. A.M. Meson, F. Vericat, J. Math. Phys. 37 (1996) 4480.
38. A.K. Rajagopal, Phys. Rev. Lett. 76 (1996) 3469.
39. A.R. Plastino, A. Plastino, Phys. Lett. A 174 (1993) 384.
40. A.R. Plastino, A. Plastino, Phys. Lett. A 193 (1994) 251.
41. V.H. Hamity, D.E. Barraco, Phys. Rev. Lett. 76 (1996) 4664.
42. D.H. Zanette, P.A. Alemany, Phys. Rev. Lett. 75 (1995) 366.
43. C. Tsallis, S.V.F. Levy, A.M.C. Souza, R. Maynard, Phys. Rev. Lett. 75 (1995) 3589.
44. A. Plastino, A.R. Plastino, Phys. Lett. A 226 (1997) 257.
45. E.M.F. Curado, in: Int. Workshop on the Foundations of Statistical Mechanics and Thermodynamics, Natal, Brazil, October 1997.
46. E.D Malaza, F. Solms, submitted for publication.