Integral and integro-differential equations
Several applied problems are described by mathematical models defined by linear or non-linear integral or integro-differential equations of Volterra type, whose kernels can be weakly singular, or by integral equations of Fredholm type with kernels that can be singular, or even hypersingular.
For the numerical solution of these equations, numerical methods of projection or Nyström type have been proposed and constructed, using also ad hoc quadrature rules. In the case of Fredholm type integral equations, with hypersingular kernels, some of these methods have been used to solve time-harmonic electromagnetic scattering problems in waveguides, and problems of backscattering from cracks.