Abstract:
A method for the numerical solution of a class of boundary integral equations
in the plane theory of elasticity on curves forming the boundary of simply
connected polygons is proposed. Under some restrictions on geometry of
domains, we prove the existence and uniqueness of solutions to approximating
systems of linear algebraic equations. Several estimates of stability are
obtained. The exponential rate of convergence for this method is proved in
C-norm. The work was supported by the Russian Foundation for Basic Research
(99–01–01146) and by the Scientific Program “Universities of Russia”
(UR.04.03.002).
Keywords:boundary integral equations, quadrature method, plane elasticity theory, stability, linear systems.