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A heat approximation

Miroslav Dont — 2000

Applications of Mathematics

The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.

Fourier problem with bounded Baire data

Miroslav Dont — 1997

Mathematica Bohemica

The Fourier problem on planar domains with time moving boundary is considered using integral equations. Solvability of those integral equations in the space of bounded Baire functions as well as the convergence of the corresponding Neumann series are proved.

A note on the parabolic variation

Miroslav Dont — 2000

Mathematica Bohemica

A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is 1 2 -Holder. Further, some simple concrete examples are examined.

A numerical solution of the Dirichlet problem on some special doubly connected regions

Miroslav DontEva Dontová — 1998

Applications of Mathematics

The aim of this paper is to give a convergence proof of a numerical method for the Dirichlet problem on doubly connected plane regions using the method of reflection across the exterior boundary curve (which is analytic) combined with integral equations extended over the interior boundary curve (which may be irregular with infinitely many angular points).

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