NDLI: Algorithms for Symmetric Differential Systems

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Algorithms for Symmetric Differential Systems

Best Meromorphic Approximation of Markov Functions on the Unit Circle

On the Power of Standard Information for Weighted Approximation

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Algorithms for Symmetric Differential Systems

Content Provider	Springer Nature Link
Author	Mansfield, Elizabeth L.
Abstract	Over-determined systems of partial differential equations may be studied using differential—elimination algorithms, as a great deal of information about the solution set of the system may be obtained from the output. Unfortunately, many systems are effectively intractable by these methods due to the expression swell incurred in the intermediate stages of the calculations. This can happen when, for example, the input system depends on many variables and is invariant under a large rotation group, so that there is no natural choice of term ordering in the elimination and reduction processes. This paper describes how systems written in terms of the differential invariants of a Lie group action may be processed in a manner analogous to differential—elimination algorithms. The algorithm described terminates and yields, in a sense which we make precise, a complete set of representative invariant integrability conditions which may be calculated in a ``critical pair'' completion procedure. Further, we discuss some of the profound differences between algebras of differential invariants and standard differential algebras. We use the new, regularized moving frame method of Fels and Olver [11], [12] to write a differential system in terms of the invariants of a symmetry group. The methods described have been implemented as a package in \MAPLE. The main example discussed is the analysis of the (2+1 )-d'Alembert—Hamilton system u_{xx}+u_{yy}- u_{zz}&=& f(u), u_x^2+u_y^2- u_z^2&=&1. (1) We demonstrate the classification of solutions due to Collins [7] for f\ne 0 using the new methods.
Starting Page	335
Ending Page	383
Page Count	49
File Format	PDF
ISSN	16153375
Journal	Foundations of Computational Mathematics
Volume Number	1
Issue Number	4
Language	English
Publisher	Springer-Verlag
Publisher Date	2001-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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On Classes of Functions Related to Starlike Functions with Respect to Symmetric Conjugate Points Defined by a Fractional Differential Operator

Symmetric Projection Methods for Differential Equations on Manifolds

Spectral Collocation Methods for Differential-Algebraic Equations with Arbitrary Index

Algorithms for Symmetric Differential Systems

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