Spectral parameter power series method for discontinuous coefficients

Let (a,b) be a finite interval and 1/p, q, r∈L1[a,b]. We show that a general solution (in the weak sense) of the equation (pu′)′+qu = λru on (a,b) can be constructed in terms of power series of the spectral parameter λ. The series converge uniformly on [a,b] and the corresponding coefficients are co...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 38; no. 10; pp. 2000 - 2011
Main Authors Blancarte, Herminio, Campos, Hugo M., Khmelnytskaya, Kira V.
Format Journal Article
LanguageEnglish
Published Blackwell Publishing Ltd 15.07.2015
Subjects
Construction
discontinuity conditions
Eigenvalues
Mathematical analysis
Mathematical models
Power series
Recursive
Representations
Spectra
spectral parameter power series
Sturm-Liouville problems
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Summary:Let (a,b) be a finite interval and 1/p, q, r∈L1[a,b]. We show that a general solution (in the weak sense) of the equation (pu′)′+qu = λru on (a,b) can be constructed in terms of power series of the spectral parameter λ. The series converge uniformly on [a,b] and the corresponding coefficients are constructed by means of a simple recursive procedure. We use this representation to solve different types of eigenvalue problems. Several numerical tests are discussed. Copyright © 2014 John Wiley & Sons, Ltd.
Bibliography:istex:A1660C1FCB0A0C7E4CF6AA3E3A3A8AFABF96900E
ArticleID:MMA3282
ark:/67375/WNG-PG1BG4JQ-J
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3282