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

Andriy Beshley, Roman Chapko, B. Tomas Johansson*

*Corresponding author for this work

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.

Original languageEnglish
Title of host publicationTrends in Mathematics
EditorsK. Lindahl , T. Lindström, L. Rodino, J. Toft, P. Wahlberg
PublisherSpringer
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

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    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. https://doi.org/10.1007/978-3-030-04459-6_47