A factorization algorithm for linear ordinary differential equations

Authors:
F. Schwarz
Affiliations:
GMD, Institut F1, St. Augustin, W. Germany
Venue:
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Year:
1989

Citing 0
Cited 17

Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients

ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
On solutions of linear ordinary differential equations in their coefficient field

Journal of Symbolic Computation
Linear ordinary differential equations: breaking through the order 2 barrier

ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
On d'Alembert substitution

ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Efficient factorization of linear ODE's

ACM SIGSAM Bulletin
An improved algorithm for factoring linear ordinary differential operators

ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Rational solutions of the mixed differential equation and its application to factorization of differential operators

ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
An algorithm for computing exponential solutions of first order linear differential systems

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Factoring zero-dimensional ideals of linear partial differential operators

Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Factorization of the Heun's differential operator

Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Factoring systems of linear PDEs with finite-dimensional solution spaces

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Decomposition of differential polynomials with constant coefficients

ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Generalized Loewy-decomposition of d-modules

Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Solving and factoring boundary problems for linear ordinary differential equations in differential algebras

Journal of Symbolic Computation
A Symbolic Framework for Operations on Linear Boundary Problems

CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Differential and difference equations for products of classical orthogonal polynomials

CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Review of symbolic software for lie symmetry analysis

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

The reducibility and factorization of linear homogeneous differential equations are of great theoretical and practical importance in mathematics. Although it has been known for a long time that factorization is in principle a decision procedure, its use in an automatic differential equation solver requires a more detailed analysis of the various steps involved. Especially important are certain auxiliary equations, the so-called associated equations. An upper bound for the degree of its coefficients is derived. Another important ingredient is the computation of optimal estimates for the size of polynomial and rational solutions of certain differential equations with rational coefficients. Applying these results, the design of the factorization algorithm LODEF and its implementation in the Scratchpad II Computer Algebra System is described.