Albrecht, D.W. and Mansfield, E.L. and Milne, A.E. (1996) Algorithms for special integrals of ordinary differential equations. Journal of Physics a-Mathematical and General, 29 (5). pp. 973-991. ISSN 0305-4470.
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We 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 Painleve equations, and a third-order ordinary differential equation of Painleve type are investigated. We prove that for the second Painleve equation, the known special integrals are the only ones possible.
|Subjects:||Q Science > QC Physics > QC20 Mathematical Physics
Q Science > QC Physics
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||M.A. Ziai|
|Date Deposited:||17 May 2009 10:22|
|Last Modified:||17 May 2009 10:22|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/18785 (The current URI for this page, for reference purposes)|
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