Course description

Aim. Study of the approach for the reduction of differential problems to boundary integral equations.

Short description. This course is continuation of numerical methods and functional analysis courses. It includes lectures and laboratory works. Students get the knowledge about the theory of regularization for the integral equations of the first kind and the Riesz-Schauder theory for equations of the second kind, the theory of collectively compact operators, the investigation of convergence for the Nyström method and other numerical methods etc.

The laboratory works include tasks for the numerical solution of elliptic problems by integral equation approach. The full discretization is realized by the quadrature method with the use of trigonometrical interpolation. The corresponding numerical experiments are planned.

Objects. To be familiar with basic methods for the reduction of differential problems to boundary integral equations, with the investigation of the well-possedness of integral equations of the first and second kind and with numerical methods for their solution.

As result after the study student must

• know: basic steps for the application of the integral equation approach for the numerical solution of boundary value problems for elliptic equations;
• be able: to apply the integral equation method to concrete elliptic problems,  to build own program products.