Details:
Title  Generalized power series solutions to linear partial differential equations  Author(s)  Joris van der Hoeven  Type  Article in Journal  Abstract  Let 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 .  Keywords  Linear partial differential equation, Asymptotics, Algorithm, Differential algebra, Formal power series, Tangent cone algorithm  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717107000442 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  8  Pages  771  791  Year  2007  Edition  0  Translation 
No  Refereed 
No 
