Dimsym and LIE: Symmetry determination packages

Mathematical and Computer Modelling - Tập 25 Số 8-9 - Trang 153-164 - 1997
J. Sheering1, A. K. Head2, G. E. Prince1
1School of Mathematics, LaTrobe University Bundoora, Victoria 3083, Australia#TAB#
2Division of Material Science and Technology, CSIRO Locked Bag 33, Rosebank MDC, Clayton, Victoria 3169, Australia

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Tài liệu tham khảo

Head, 1993, LIE: A PC program for Lie analysis of differential equations, Comp. Phys. Comm., 77, 241, 10.1016/0010-4655(93)90007-Y

Sherring, 1993, Dimsym: Symmetry determination and linear differential equations package

Sherring, 1993, Symmetry and computer algebra techniques for differential equations

Bluman, 1989, Symmetries and differential equations, Applied Mathematical Sciences, 81

Olver, 1986

Schwarz, 1988, Symmetries of differential equations: From Sophus Lie to computer algebra, Siam Rev., 30, 450, 10.1137/1030094

Stephani, 1989, Differential Equations: Their Solution Using Symmetries

Hereman, 1993, Review of symbolic software for computation of Lie symmetries of differential equations, Euromath Bulletin, 2

Reid, 1991, Finding abstract Lie symmetry algebras of differential equations without integrating determining equations, European J. Appl. Math., 2, 319, 10.1017/S0956792500000589

Hearn, 1995

Schrüfer, 1995, EXCALC: A System for Doing Calculations in the Calculus of Modern Differential Geometry

Kersten, 1987, Infinitesimal symmetries: A computational approach

Schwarz, 1985, Automatically determining symmetries of partial differential equations, Computing, 34, 91, 10.1007/BF02259838

Reid, 1990, A triangularization algorithm which determines the Lie symmetry algebra of any system of PDEs, J. Phys. A, 23, L853, 10.1088/0305-4470/23/17/001

Reid, 1991, Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution, Euro. Jnl. of Applied Mathematics, 2, 293, 10.1017/S0956792500000577

Janet, 1920, Sur les systèmes d'équations aux dérivées partielles, Journal de Mathematique, 8III, 65

Schwarz, 1984, The Riquier-Janet theory and its application to nonlinear evolution equations, Phys. D, 11, 243, 10.1016/0167-2789(84)90447-0

MacCallum, 1995, ODESOLVE

Reid, 1993

Hill, 1988

Kersten, 1989, Software to compute infinitesimal symmetries of exterior systems, with applications, Acta Appl. Math., 16, 207, 10.1007/BF00046573

Schwarz, 1995, REDUCE 3.6 Miscellaneous Documentation