The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations

摘要: Here we present a fully discretized projection method with Fourier series which is based on modification of the fast transform. The applied to systems integro-differential equations Cauchy kernel, boundary integral from element and, more generally, certain elliptic pseudodifferential closed smooth curves. We use Gaussian quadratures families equidistant partitions combined This yields an extremely accurate and numerical scheme. complete asymptotic error estimates including quadrature errors. These are quasioptimal exponential order for analytic data. Numerical experiments scattering problem, clamped plate plane estatostatics confirm theoretical convergence rates show high accuracy.