1 research outputs found
Anti-Gauss cubature rules with applications to Fredholm integral equations on the square
The purpose of this paper is to develop the anti-Gauss cubature rule for
approximating integrals defined on the square whose integrand function may have
algebraic singularities at the boundaries. An application of such a rule to the
numerical solution of second-kind Fredholm integral equations is also explored.
The stability, convergence, and conditioning of the proposed Nystr\"om-type
method are studied. The numerical solution of the resulting dense linear system
is also investigated and several numerical tests are presented