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Chow, Shui-Nee; Drachman, Byron; Wang, Duo

Computation of normal forms. (English) Zbl 0687.65075

J. Comput. Appl. Math. 29, No. 2, 129-143 (1990).
The computation of normal (i.e. simple or canonical) forms for a differential system is particularly useful in nonlinear dynamics problems. The method of R. H. Rand and W. L.Keith [Applications of computer algebra, 309-328 (1985; Zbl 0653.65004)] is simple but assumes that the “form” of a fixed normal form is already known. Related to it, the present paper gives: first, a method and a program to compute the “form” of a fixed normal form; after, a method to compute the normal form for the differential system (having computed the normal form for the matrix of the linear term). A program using the symbolic manipulator MACSYMA is applied in several examples.
Reviewer: A.de Castro

Cited in 14 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
68W30 Symbolic computation and algebraic computation
37-XX Dynamical systems and ergodic theory
34A34 Nonlinear ordinary differential equations and systems

Keywords:

symbolic computation; numerical examples; differential system; nonlinear dynamics; computer algebra; normal form; program; symbolic manipulator MACSYMA

Citations:

Zbl 0653.65004

Software:

MACSYMA
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Full Text: DOI

References:

[1] Arnold, V., Geometrical Methods in the Theory of Ordinary Differential Equations (1982), Springer: Springer New York
[2] Chow, S.-N.; Hale, J. K., Methods of Bifurcation Theory (1982), Springer: Springer New York · Zbl 0487.47039
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[7] M.D. Kruskal and H. Segur, Asymptotics beyond all orders in a model of dentrites, to appear.; M.D. Kruskal and H. Segur, Asymptotics beyond all orders in a model of dentrites, to appear. · Zbl 0732.34047
[8] R.H. Rand and W.L. Keith, Normal forms and center manifold calculation on MACSYMA, in: R. Pavelle, Ed., Applications of Computer Algebra.; R.H. Rand and W.L. Keith, Normal forms and center manifold calculation on MACSYMA, in: R. Pavelle, Ed., Applications of Computer Algebra.
[9] Takens, F., Singularities of vector fields, Publ. Math. Inst. Hautes Etades Sci., 43, 47-100 (1974) · Zbl 0279.58009
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