Singer and Ulmer (1997) gave an algorithm to compute Liouvillian ("closed-form") solutions of homogeneous linear differential equations. However, there were several efficiency problems that made computations often not practical. In this paper we address these problems. We extend the algorithm in
Overconvergence Phenomena and Grouping in Exponential Representation of Solutions of Linear Differential Equations of Infinite Order
β Scribed by Takahiro Kawai; Daniele C. Struppa
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 113 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0001-8708
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π SIMILAR VOLUMES
## Abstract We study the existence of solutions of the general elliptic system of partial differential equations in the space where the principal part may be represented with the help of a CLIFFORDalgebra π. We construct an integral representation and discuss the properties of the kernels.
The explicit closed-form solutions for a second-order differential equation with a constant self-adjoint positive definite operator coefficient A (the hyperbolic case) and for the abstract Euler-Poisson-Darboux equation in a Hilbert space are presented. On the basis of these representations, we prop