On numerical methods for hamiltonian PDEs and a collocation method for the Vlasov-Maxwell equations

Journal of Computational Physics

Volumn 129, Issue 1, 1996, Pages 121-133

  Holloway, James Paul ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE EVENT SIMULATION; MAXWELL EQUATIONS; NUMERICAL METHODS; PHYSICAL PROPERTIES; VLASOV EQUATION;

CASIMIR; COLLOCATION METHOD; CONSERVATION LAW; DISCRETIZATIONS; HAMILTONIAN PDES; HAMILTONIAN STRUCTURES; LAW CONSTANTS; METHOD OF LINES; VLASOV-MAXWELL EQUATIONS; WEIGHTED RESIDUALS METHOD;

HAMILTONIANS;

EID: 0030295549     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0238     Document Type: Article

References (22)

1. 1. P. J. Morrison, Phys. Lett. A 80, 383 (1980).
2. 2. J. E. Marsden and A. Weinstein, Physica D 4, 394 (1982).
3. 3. D. D. Holm, J. E. Marsden, T. Ratiu, and A. Weinstein, Phys. Rep. 123, 1 (1985).
4. 4. T. Shepherd, Adv. Geophys. 32, 287 (1990).
5. 5. D. Greenspan, J. Comput. Phys. 56, 28 (1984).
6. 6. J. M. Snaz-Serna, BIT 28, 877 (1988).
7. 7. F. M. Lasagni, J. Appl. Math. Phys. 39, 952 (1988).
8. 8. P. J. Channell and C. Scovel, Nonlinearity 3, 231 (1990).
9. 9. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980).
10. 10. P. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, Berlin, 1986).
11. 11. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Springer-Verlag, Berlin, 1994).
12. 12. C. S. Gardner, J. Math. Phys. 12, 1548 (1971).
13. 13. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (SIAM, Philadelphia, 1977).
14. 14. D. Gottlieb, M. Y. Hussaini, and S. A. Orszag, "Theory and Applications of Spectral Methods," in Spectral Methods for Partial Differential Equations, edited by R. G. Voigt, D. Gottlieb, and M. Y. Hussaini (SIAM, Philadelphia, 1984).
15. 15. S. B. Wineberg, J. F. McGrath, E. F. Gabl, L. R. Scott, and C. E. Southwell, J. Comput. Phys. 97, 311 (1991).
16. 16. J. de Frutos, T. Ortega, and J. M. Sanz-Serna, Comput. Methods Appl. Mech. Eng. 80, 417 (1990).
17. 17. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
18. 18. A. Vlasov, J. Phys. 9, 25 (1945).
19. 19. J. P. Holloway, Trans. Am. Nucl. Soc. 69, 232 (1993).
20. 20. H. R. Lewis, J. Comput. Phys. 6, 136 (1970).
21. 21. H. R. Lewis, J. Comput. Phys. 10, 400 (1972).
22. 22. C. Scovel and A. Weinstein, Commun. Pure Appl. Math. 47, 683 (1994).