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TitleGeneralized power series solutions to linear partial differential equations
Author(s) Joris van der Hoeven
TypeArticle in Journal
AbstractLet Θ = C [ e − x 1 , , e − x n ] [ ∂ 1 , , ∂ n ] and S = C [ x 1 , , x n ] [ [ e C x 1 + ⋯ + C x n ] ] , where C is an effective field and x 1 N ⋯ x n N e C x 1 + ⋯ + C x n and S are given a suitable asymptotic ordering ≼ . Consider the mapping L : S → S l ; f ↦ ( L 1 f , , L l f ) , where L 1 , , L l ∈ Θ . For g = ( g 1 , , g l ) ∈ S L l = im L , it is natural to ask how to solve the system L f = g . In this paper, we will effectively characterize S L l and show how to compute a so called distinguished right inverse L − 1 : S L l → S of L . We will also characterize the solution space of the homogeneous equation L h = 0 .
KeywordsLinear partial differential equation, Asymptotics, Algorithm, Differential algebra, Formal power series, Tangent cone algorithm
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717107000442
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number8
Pages771 - 791
Year2007
Edition0
Translation No
Refereed No
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