Formal Algorithmic Elimination for PDEs
Abstract
Similarly to the correspondence between radical ideals of a polynomial ring and varieties in algebraic geometry, a correspondence between radical differential ideals and their analytic solution sets has been established in differential algebra. This tutorial discusses aspects of this correspondence involving symbolic computation. In particular, an introduction to the Thomas decomposition method is given. It splits a system of polynomially nonlinear partial differential equations into finitely many so-called simple differential systems whose solution sets form a partition of the original solution set. The power series solutions of each simple system can be determined in a straightforward way. Conversely, certain sets of analytic functions admit an implicit description in terms of partial differential equations and inequations. Strategies for solving related differential elimination problems and applications to symbolic solving of differential equations are presented. A Maple implementation of the Thomas decomposition method is freely available.
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Published In
July 2016
434 pages
ISBN:9781450343800
DOI:10.1145/2930889
- General Chairs:
- Sergei Abramov,
- Eugene Zima,
- Program Chair:
- Xiao-Shan Gao
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Published: 20 July 2016
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ISSAC '16: International Symposium on Symbolic and Algebraic Computation
July 20 - 22, 2016
ON, Waterloo, Canada
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