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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Published in | Mathematical methods in the applied sciences Vol. 38; no. 10; pp. 2000 - 2011 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Blackwell Publishing Ltd
15.07.2015
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Subjects | |
Online Access | Get full text |
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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. |
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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 |