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On a generalization of neumann series of bessel functions using Hessenberg matrices and matrix exponentials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-9443-8772
2019 (English)In: European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Springer, 2019, Vol. 126, p. 205-214Conference paper, Published paper (Refereed)
Abstract [en]

The Neumann expansion of Bessel functions (of integer order) of a function g: ℂ→ ℂ corresponds to representing g as a linear combination of basis functions φ0, φ1, …, i.e., g(s)=∑ℓ=0 ∞wℓφℓ(s), where φi(s) = Ji(s), i = 0, …, are the Bessel functions. In this work, we study an expansion for a more general class of basis functions. More precisely, we assume that the basis functions satisfy an infinite dimensional linear ordinary differential equation associated with a Hessenberg matrix, motivated by the fact that these basis functions occur in certain iterative methods. A procedure to compute the basis functions as well as the coefficients is proposed. Theoretical properties of the expansion are studied. We illustrate that non-standard basis functions can give faster convergence than the Bessel functions.

Place, publisher, year, edition, pages
Springer, 2019. Vol. 126, p. 205-214
Series
Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 126
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-241801DOI: 10.1007/978-3-319-96415-7_17Scopus ID: 2-s2.0-85060038484ISBN: 9783319964140 (print)OAI: oai:DiVA.org:kth-241801DiVA, id: diva2:1282700
Conference
European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway, 25 September 2017 through 29 September 2017
Note

QC 20190125

Available from: 2019-01-25 Created: 2019-01-25 Last updated: 2019-01-25Bibliographically approved

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Koskela, AnttiJarlebring, Elias

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