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

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.