On the numerical solution of parabolic Cauchy problem in a domain with cut (in Ukrainian)

Author V. G. Vavrychuk, R. S. Chapko

Ivan Franko National University of Lviv

Abstract Cauchy problem is numerically solved with help of iterative regularization procedure at every step of which mixed nonstationary Dirichlet-Neumann problems for parabolic equation arise. Using Rothe’s method mixed problems are reduced to the boundary integral equations which have three kinds of singularities: square root, logarithmic and hypersingularity. Special techniques are employed to cope with them so that in the case of analytic input data solution of boundary integral equations have exponential error decay.
Keywords heat equation; Cauchy problem; Ladweber method; mixed boundary value problems; single- and double layer potentials; integral equation of the first kind; trigonometrical quadrature method
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Pages 209-218
Volume 37
Issue 2
Year 2012
Journal Matematychni Studii
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