### 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.

Language | English |
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Title of host publication | Trends in Mathematics |

Editors | K. Lindahl , T. Lindström, L. Rodino, J. Toft, P. Wahlberg |

Publisher | Springer International Publishing AG |

Pages | 493-501 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-030-04459-6 |

ISBN (Print) | 978-3-030-04458-9 |

DOIs | |

Publication status | E-pub ahead of print - 30 Apr 2019 |

### Publication series

Name | Trends in Mathematics |
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ISSN (Print) | 2297-0215 |

ISSN (Electronic) | 2297-024X |

### Fingerprint

### Cite this

*Trends in Mathematics*(pp. 493-501). (Trends in Mathematics). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-04459-6_47

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients

AU - Beshley, Andriy

AU - Chapko, Roman

AU - Johansson, B. Tomas

PY - 2019/4/30

Y1 - 2019/4/30

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85065389071&partnerID=8YFLogxK

UR - https://link.springer.com/chapter/10.1007%2F978-3-030-04459-6_47

U2 - 10.1007/978-3-030-04459-6_47

DO - 10.1007/978-3-030-04459-6_47

M3 - Chapter

SN - 978-3-030-04458-9

T3 - Trends in Mathematics

SP - 493

EP - 501

BT - Trends in Mathematics

A2 - Lindahl , K.

A2 - Lindström, T.

A2 - Rodino, L.

A2 - Toft, J.

A2 - Wahlberg, P.

PB - Springer International Publishing AG

ER -