A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients

Andriy Beshley, Roman Chapko, B. Tomas Johansson

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.

LanguageEnglish
Title of host publicationTrends in Mathematics
EditorsK. Lindahl , T. Lindström, L. Rodino, J. Toft, P. Wahlberg
PublisherSpringer International Publishing AG
Pages493-501
Number of pages9
ISBN (Electronic)978-3-030-04459-6
ISBN (Print)978-3-030-04458-9
DOIs
Publication statusE-pub ahead of print - 30 Apr 2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Fingerprint

Integral Equation Method
Variable Coefficients
Elliptic Problems
Cauchy Problem
Integral Equations
Second Order Elliptic Equations
Tikhonov Regularization
Integral domain
Numerical Approximation
Numerical Investigation
Cauchy
Divergence
Unknown
Dependent
Coefficient

Cite this

Beshley, A., Chapko, R., & Johansson, B. T. (2019). A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. In K. Lindahl , T. Lindström, L. Rodino, J. Toft, & P. Wahlberg (Eds.), Trends in Mathematics (pp. 493-501). (Trends in Mathematics). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-04459-6_47
Beshley, Andriy ; Chapko, Roman ; Johansson, B. Tomas. / A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. Trends in Mathematics. editor / K. Lindahl ; T. Lindström ; L. Rodino ; J. Toft ; P. Wahlberg. Springer International Publishing AG, 2019. pp. 493-501 (Trends in Mathematics).
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Beshley, A, Chapko, R & Johansson, BT 2019, A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. in K Lindahl , T Lindström, L Rodino, J Toft & P Wahlberg (eds), Trends in Mathematics. Trends in Mathematics, Springer International Publishing AG, pp. 493-501. https://doi.org/10.1007/978-3-030-04459-6_47

A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. / Beshley, Andriy; Chapko, Roman; Johansson, B. Tomas.

Trends in Mathematics. ed. / K. Lindahl ; T. Lindström; L. Rodino; J. Toft; P. Wahlberg. Springer International Publishing AG, 2019. p. 493-501 (Trends in Mathematics).

Research output: Chapter in Book/Report/Conference proceedingChapter

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AB - We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.

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Beshley A, Chapko R, Johansson BT. A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. In Lindahl K, Lindström T, Rodino L, Toft J, Wahlberg P, editors, Trends in Mathematics. Springer International Publishing AG. 2019. p. 493-501. (Trends in Mathematics). https://doi.org/10.1007/978-3-030-04459-6_47