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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 248, Pages 86–93 (Mi tm121)  
A Block Method for Solving the Laplace Equation in a Disk with a Hole That Has Cuts

E. A. Volkov

Steklov Mathematical Institute, Russian Academy of Sciences
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Abstract: A numerical–analytic block method proposed by the author is applied to construct an approximate solution to the Dirichlet problem for the Laplace equation in a disk with an elliptic hole that has two cuts. The construction employs two blocks–rings and an elementary conformal mapping. It is shown that the approximate solution converges, in the uniform metric, exponentially with respect to the order of a rapidly solvable system of linear algebraic equations.
Received in October 2004
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Document Type: Article
Language: Russian
Citation: E. A. Volkov, “A Block Method for Solving the Laplace Equation in a Disk with a Hole That Has Cuts”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 248, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 86–93; Proc. Steklov Inst. Math., 248 (2005), 81–88
Citation in format AMSBIB
\Bibitem{Vol05}
\by E.~A.~Volkov
\paper A~Block Method for Solving the Laplace Equation in a~Disk with a~Hole That Has Cuts
\inbook Studies on function theory and differential equations
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 248
\pages 86--93
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm121}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2165918}
\zmath{https://zbmath.org/?q=an:1152.35340}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 248
\pages 81--88
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