Examples of the investigation of differential equations with modularized programs

Mathematical and Computer Modelling

Volumn 25, Issue 8-9, 1997, Pages 133-139

  Wolf, T ^a   Brand, A ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Conservation laws; Differential equations; Lie symmetries; Space time symmetries; Variational principle

Indexed keywords

ALGEBRA; ALGORITHMS; CALCULATIONS; COMPUTER SOFTWARE; FUNCTIONS; INTEGRATION; NUMERICAL METHODS; VARIATIONAL TECHNIQUES;

COMPUTER ALGEBRA SOFTWARE; EVOLUTIONARY EQUATIONS; LIE SYMMETRIES;

DIFFERENTIAL EQUATIONS;

EID: 0031127955     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(97)00064-2     Document Type: Article

References (18)

1. J. Kovacic, An algorithm for solving second order linear homogeneous differential equations, J. Symb. Comp. 2 (1986).
2. th order linear differential equations, Am. J. Math. 103 (1981).
3. F. Ulmer, On Liouvillian solutions of differential equations, J. Appl in Eng. Comm. and Comp. 2 (1992).
4. W. Hereman, CRC Handbook of Lie Group Analysis of Differential Equations, (Edited by N.H. Ibragimov), Volume 3, CRC Press, (1995).
5. T. Wolf and A. Brand, The computer algebra package CRACK for investigating PDEs, Manual for the Package CRACK in the REDUCE Network Library; In Proceedings of ERCIM School on Partial Differential Equations and Group Theory, Bonn, April 1992, GMD, Bonn.
6. T. Wolf and A. Brand, Investigating DEs with CRACK and related programs, Special issue of SIGSAM Bulletin 1-8 (June 1995).
7. V.V. Sokolov and S.I. Svinolupov, Mat. Zametki 40, 91 (1990).
8. V.V. Sokolov, S.I. Svinolupov and T. Wolf, Linearizable evolutionary equations of second order, Physics Letters A 163, 415 (1992).
9. A. Bocharov, DELiA 1.5.11 User Guide, (1991).
10. W.D. Drechsler, Class. Quant. Grav. 6, 623-657 (1989).
11. H. Melenk, The complexity barrier in REDUCE: A case study, Technical Report TR 94-6, Konrad-Zuse-Zentrum Berlin (1994).
12. M. Kubitza, FSU Jena, private communication.
13. T. Wolf, Programs for applying symmetries of PDEs, In Proceedings of ISSAC 95, p. 7, ACM Press, (1995).
14. C. Herssens and P. Bonckaert, Limburgs Universitair Centrum/Belgium, private communication.
15. T. Wolf and G. Grebot, Automatic symmetry investigation of space-time metrics, Int. J. of Mod. Phys. D 3 (1) (1994).
16. E. Kamke, Lösungsmethoden und Lösungen von Differentialgleichungen, Partielle Differentialgleichungen erster Ordnung, B.G. Teubner, Stuttgart, (1979).
17. T. Wolf, An efficiency improved program LIEPDE for determining Lie-symmetries of PDEs, In Proceedings of the Workshop on Modern Group Theory Methods, Acireale, Sicily, November, 1992.
18. V.I. Karpman, Phys. Lett. A 136, 216 (1989).