Chapko R. A numerical solution of the linear direct and non-linear inverse evolution problems.

The dissertation is concerned with the numerical solution of the direct and inverse evolution problems by boundary integral equation method. For the numerical solution of initial boundary value problems in unbounded domains the combination of Rothe's method or Laguerre transformation with respect to time and boundary integral equation method are applied. The full discretization is made by quadrature method based on the trigonometrical interpolation. The convergence analysis and error estimate are shown. This approach is generalized for the boundary value problems in elasticity. We considered the numerical solution of evolution problem with first and second time derivatives on a manifold by integral equation method. The uniqueness of the solution and the differentiability of the corresponding nonlinear operators with respect to the interior boundary curve have been established. The numerical solution is realized by the regularized Newton and Landweber methods and gibrid method with combination of the boundary integral equation.