Geodesic
A~Block Method for Solving the Laplace Equation in a~Disk with a~Hole That Has Cuts
Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 86-93

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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. 
@article{TRSPY_2005_248_a8,
     author = {E. A. Volkov},
     title = {A~Block {Method} for {Solving} the {Laplace} {Equation} in {a~Disk} with {a~Hole} {That} {Has} {Cuts}},
     journal = {Informatics and Automation},
     pages = {86--93},
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     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a8/}
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E. A. Volkov. A~Block Method for Solving the Laplace Equation in a~Disk with a~Hole That Has Cuts. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 86-93. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a8/