Polynomial general solutions for first order autonomous ODEs

Authors:
Ruyong Feng;Xiao-Shan Gao
Affiliations:
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Academia Sinica, Beijing, P. R. China;Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Academia Sinica, Beijing, P. R. China
Venue:
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Year:
2004

Citing 14
Cited 0

An algorithm for solving second order linear homogeneous differential equations

Journal of Symbolic Computation
On Liouvillian solutions of homogeneous linear differential equations

ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
On solutions of linear ordinary differential equations in their coefficient field

Journal of Symbolic Computation
The general solution of an ordinary differential equation

ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
About the polynomial solutions of homogeneous linear differential equations depending on parameters

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
An algorithm computing the regular formal solutions of a system of linear differential equations

Journal of Symbolic Computation - Special issue on differential algebra and differential equations
Rational solutions of Riccati-like partial differential equations

Journal of Symbolic Computation
On Liouvillian solutions of linear differential equations of order 4 and 5

Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Polynomial Algorithms in Computer Algebra

Polynomial Algorithms in Computer Algebra
Taylor polynomial solutions of linear differential equations

Applied Mathematics and Computation
Polynomial solutions for first order ODEs with constant coefficients

ACM SIGSAM Bulletin
Rational general solutions of algebraic ordinary differential equations

ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Galois theory and algorithms for linear differential equations

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

For a first order autonomous ODE, we give a polynomial time algorithm to decide whether it has a polynomial general solution and to compute one if it exists. Experiments show that this algorithm is quite effective in solving ODEs with high degrees and a large number of terms.