Solution the Dirichlet Problem for Multiply Connected Domain Using Numerical Conformal Mapping
Publication type: Journal Article
Publication date: 2019-01-01
scimago Q2
wos Q2
SJR: 0.545
CiteScore: 1.2
Impact factor: 0.8
ISSN: 16618254, 16618262
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics
Abstract
We present a method for construction of continuous approximate 2D Dirichlet problems solutions in an arbitrary multiply connected domain with a smooth boundary. The method is based on integral equations solution which is reduced to a linear system solution and does not require iterations. Unlike the Fredholm’s solution of the problem ours applies not a logarithsmic potential of a double layer but the properties of Cauchy integral boundary values. We search for the solution of the integral equation in the form of Fourier polynomial with the coefficients being the solution of a linear equation system. The continuous solution of Dirichlet problem is the real part of a Cauchy integral.
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Abzalilov D. F., Ivanshin P., Shirokova E. Solution the Dirichlet Problem for Multiply Connected Domain Using Numerical Conformal Mapping // Complex Analysis and Operator Theory. 2019. Vol. 13. No. 3. pp. 1419-1429.
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Abzalilov D. F., Ivanshin P., Shirokova E. Solution the Dirichlet Problem for Multiply Connected Domain Using Numerical Conformal Mapping // Complex Analysis and Operator Theory. 2019. Vol. 13. No. 3. pp. 1419-1429.
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TY - JOUR
DO - 10.1007/s11785-018-00882-y
UR - https://doi.org/10.1007/s11785-018-00882-y
TI - Solution the Dirichlet Problem for Multiply Connected Domain Using Numerical Conformal Mapping
T2 - Complex Analysis and Operator Theory
AU - Abzalilov, D F
AU - Ivanshin, Pyotr
AU - Shirokova, E.A.
PY - 2019
DA - 2019/01/01
PB - Springer Nature
SP - 1419-1429
IS - 3
VL - 13
SN - 1661-8254
SN - 1661-8262
ER -
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@article{2019_Abzalilov,
author = {D F Abzalilov and Pyotr Ivanshin and E.A. Shirokova},
title = {Solution the Dirichlet Problem for Multiply Connected Domain Using Numerical Conformal Mapping},
journal = {Complex Analysis and Operator Theory},
year = {2019},
volume = {13},
publisher = {Springer Nature},
month = {jan},
url = {https://doi.org/10.1007/s11785-018-00882-y},
number = {3},
pages = {1419--1429},
doi = {10.1007/s11785-018-00882-y}
}
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Abzalilov, D. F., et al. “Solution the Dirichlet Problem for Multiply Connected Domain Using Numerical Conformal Mapping.” Complex Analysis and Operator Theory, vol. 13, no. 3, Jan. 2019, pp. 1419-1429. https://doi.org/10.1007/s11785-018-00882-y.
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