Numerical conformal mapping of doubly connected regions onto a disc with a circular slit
An integral equation method based on the Neumann kernel for conformal mapping f(z) of doubly connected regions onto a unit disc with a circular slit of radius µ < 1 is presented. The theoretical development is based on the boundary integral equation for conformal mapping of doubly connected re...
| Main Authors: | , , |
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| Format: | Article |
| Published: |
Penerbit ukm
2008
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| Online Access: | http://journalarticle.ukm.my/1874/ http://journalarticle.ukm.my/1874/ |
| Summary: | An integral equation method based on the Neumann kernel for conformal mapping f(z) of
doubly connected regions onto a unit disc with a circular slit of radius µ < 1 is presented. The
theoretical development is based on the boundary integral equation for conformal mapping of
doubly connected region in an earlier work of the authors. In this paper, a related system of
integral equations is constructed that is satisfied by f '(z) and µ. For numerical experiment,
the integral equation is discretised which leads to a system of nonlinear equations. The system
obtained is solved simultaneously using Gauss-Newton method. Numerical implementation on
a circular annulus is also presented |
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