A. Dzhishkariani

Approximate Solution of One Class of Singular Integral Equations by Means of Projective and Projective-Iterative Methods

abstract:
We consider singular integral equations when the line of integration is the segment $[-1,1]$. Equations are considered in the weight spaces.

For the indices $\varkappa=1$ and $\varkappa=-1$ there are additional conditions which are approximated additionally by other authors. For the index $\varkappa=1$ we narrow the domain of definition of the singular operator, while for the index $\varkappa=-1$ we narrow the range of values of the singular operator. Such a procedure allows one to justify approximate schemes without any difficulty.

Projective-iterative schemes are considered, their convergence is proved and the convergence order is determined. Stability of the projective-iterative schemes is defined and proved.

Mathematics Subject Classification: 65R20

Key words and phrases: Singular integral equation, projective and projective-iterative methods, convergence and order of convergence of approximate methods, stability