Hereman, W., Review of symbolic software for Lie symmetry analysis, Math. Comput. Model., 25(1997), 115--132. Home/Search Document Details and Download
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Symmetries and First Order ODE Patterns - Cheb-Terrab, Roche (1998) (Correct)
....determining PDE consists of restricting the cases handled to the universe of ODEs having point symmetries, so that the in nitesimals depend on just two variables, and then the determining PDE splits into a system of PDEs. Although the solving of such a PDE system may be a major problem in itself [5], the hope is that one will be able to solve it by taking advantage of the fact that it is overdetermined. For rst order ODEs, however, this strategy of splitting the determining PDE is inapplicable, so that in this case most of the computer algebra implementations of Lie methods just do not ....
W. Hereman, Review of Symbolic Software for Lie Symmetry Analysis, Mathematical and Computer Modeling, Vol. 20, Special Issue on Algorithms for Nonlinear Systems (1995).
Computer Algebra Solving of First Order ODEs Using.. - Cheb-Terrab, Duarte, Mota (1997) (Correct)
....for ODEs has already been implemented in almost all symbolic computation systems. However, though Lie s discovery of symmetry methods (SM) put most of the known solving methods under a common umbrella[1, 2, 3] only a few of the computer algebra standard solvers use SM in their solving schemes[4], and almost none use them for solving 1 st order ODEs. Generally speaking, one of the reasons for this is that the use of SM requires the solving of a system of partial di erential equations (PDEs) for the coecients of the in nitesimal symmetry generators (in nitesimals) whose solution is ....
.... of the reasons for this is that the use of SM requires the solving of a system of partial di erential equations (PDEs) for the coecients of the in nitesimal symmetry generators (in nitesimals) whose solution is not obvious, thus involving the programming of semi systematic heuristic methods [4]. Also, though in the speci c case of 1 st order ODEs we just need to solve a single 1 st order PDE, one may think that SM are useless anyway, since to use heuristics to solve that PDE may not be simpler than to guess an equivalent integrating factor for the original ODE [5] However, ....
W. Hereman, Review of Symbolic Software for Lie Symmetry Analysis, Mathematical and Computer Modeling, Vol. 20, Special Issue on Algorithms for Nonlinear Systems (1995).
Integrability Tests for Nonlinear Evolution Equations - Hereman, Göktas (1999) (2 citations) Self-citation (Hereman) (Correct)
....for the computation of recursion operators, based on the knowledge of a few conserved densities and symmetries. The computation of Lie point symmetries and generalized symmetries via prolongation techniques is purposely omitted. That topic and related software were covered extensively in [21, 22]. Space limitations also prevent the inclusion of the wellknown Painlev e test, which is a widely applied and successful integrability detector for nonlinear ODEs and PDEs. We refer to [23] for survey papers, books, and software related to Painlev e analysis. This chapter is organized as follows. ....
....can be computed with prolongation methods, and numerous software packages are available that can aid in the tedious computations inherent to such methods. A 50 page survey of software for Lie symmetry computations, including generalized symmetries, can be found in [21] and a short update in [22]. We will not repeat these software reviews here. A survey of packages for conservation laws was rst given in [15] However, to keep this chapter self contained, we present a summary of that survey. Based on dilation invariance, Ito s programs in REDUCE (see [25, 26, 27] compute polynomial ....
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W. Hereman, Review of symbolic software for Lie symmetry analysis, Mathematical and Computer Modelling 25 (1997) 115-132.
Algorithmic Computation of Generalized Symmetries of.. - Göktas, Hereman (1999) Self-citation (Hereman) (Correct)
....Higher order symmetries can be computed with prolongation methods and numerous software packages are available that can aid in the tedious computations inherent to such methods. An extensive review of software for Lie symmetry computations, including generalized symmetries, can be found in [26, 27]. With prolongation methods one generates and subsequently reduces and solves a determining system of linear homogeneous partial di erential equations for the coecients of the unknown higher order symmetry generator. In many cases, due to the length and complexity of that system, the general ....
....ansatz for the symmetry. Although restricted to polynomial higher order symmetries, we believe that the method presented in this paper is much more straightforward. Furthermore, it avoids the application of prolongation methods or Lie algebraic techniques. To avoid retreading the surveys [26, 27], we restrict our discussion to algorithms and symbolic packages that allow one to compute generalized symmetries of PDEs, as they were de ned in Section 2.1. We are not aware of software packages for DDEs to calculate directly the type of symmetries de ned in Section 3.1. Yamilov and co workers ....
W. Hereman, Review of symbolic software for Lie symmetry analysis, Mathl. Comput. Modelling, 25 (1997) 115-132.
Solutions Of Partial Differential Equations Using Symmetry And.. - Barco (2000) (Correct)
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Hereman, W., Review of symbolic software for Lie symmetry analysis, Math. Comput. Model., 25(1997), 115--132.
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