Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0916.34021
Albrecht, David W.; Mansfield, Elizabeth L.; Milne, Alice E.
Algorithms for special integrals of ordinary differential equations. (English)
[J] J. Phys. A, Math. Gen. 29, No.5, 973-991 (1996). ISSN 0305-4470

Summary: The authors give new, conceptually simple procedures for calculating special integrals of polynomial type (also known as Darboux polynomials, algebraic invariant curves, or eigenpolynomials) for ordinary differential equations. In principle, the method requires only that the given ordinary differential equation be itself of polynomial type of degree one and any order. The method is algorithmic, is suited to the use of computer algebra, and does not involve solving large nonlinear algebraic systems. To illustrate the method, special integrals of the second, fourth and sixth Painlevé equations, and a third-order ordinary differential equation of Painlevé type are investigated. They prove that for the second Painlevé equation the known special integrals are the only ones possible.

MSC 2000:: *34A45 Theoretical approximation of solutions of ODE
68W30 Symbolic computation and algebraic computation
34A99 General theory of ODE
65J99 Numerical analysis in abstract spaces

Keywords: special integrals; polynomial type; Darboux polynomials; algebraic invariant curves; eigenpolynomials; ordinary differential equations; second, fourth and sixth Painlevé equations

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]