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Approximation methods for the Muskhelishvili equation on smooth curves

Authors: V. Didenko and E. Venturino
Journal: Math. Comp. 76 (2007), 1317-1339
MSC (2000): Primary 65R20
Published electronically: February 23, 2007
MathSciNet review: 2299776
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Abstract: We investigate the possibility of applying approximation methods to the famous Muskhelishvili equation on a simple closed smooth curve $ \Gamma $. Since the corresponding integral operator is not invertible the initial equation has to be corrected in a special way. It is shown that the spline Galerkin, spline collocation and spline qualocation methods for the corrected equation are stable, and the corresponding approximate solutions converge to an exact solution of the Muskhelishvili equation in appropriate norms. Numerical experiments confirm the effectiveness of the proposed methods.

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Additional Information

V. Didenko
Affiliation: Mathematics Department, University of Brunei Darussalam, Tungku BE 1410, Brunei

E. Venturino
Affiliation: Dipartimento di Matematica, Universitá di Torino, via Carlo Alberto 10, 10123 Torino, Italy

Received by editor(s): January 26, 2006
Received by editor(s) in revised form: June 20, 2006
Published electronically: February 23, 2007
Additional Notes: The first author thanks INDAM for the support provided to him during his June 2002 visit to the University of Torino, where most of this research was carried out. He was also partially supported by UBD via Grant UBD/PNC2/2/RG/1(49)
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.