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2019 | OriginalPaper | Chapter

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

Authors : Andriy Beshley, Roman Chapko, B. Tomas Johansson

Published in: Analysis, Probability, Applications, and Computation

Publisher: Springer International Publishing

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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.

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previous chapter Boundary-Domain Integral Equations for Variable Coefficient Dirichlet BVP in 2D Unbounded Domain
next chapter On Indirect Boundary Integral Equation Methods and Applications
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Metadata
Title
A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients
Authors
Andriy Beshley
Roman Chapko
B. Tomas Johansson
Copyright Year
2019
Book
Analysis, Probability, Applications, and Computation

Print ISBN: 978-3-030-04458-9

Electronic ISBN: 978-3-030-04459-6

Copyright Year: 2019

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

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