Order-optimal methods for integro-differential equations in the singular case (Q507717)

The paper is concerned with a linear integro-differential equation of the third kind with a coefficient which has zeros of finite orders. The aim of the paper is to consider a new type of spline approximation based on generalised functions derived from the Dirac delta function. The author considers a generalised polygonal method and a generalised parabolic spline subdomain method, provides an error estimate for approximate solutions, and explores the optimisation of direct projection methods for third kind equations.