COLLOCATION METHODS FOR VOLTERRA INTEGRAL-EQUATIONS OF THE 1ST KIND

It has been shown that if a Volterra integral equation of the first kind with continuous kernel is solved numerically in a given interval I by collocation in the space of piecewise polynomials of degree m≧0 and possessing finite discontinuities at their knots ZN then a careful choice of the collocation points yields convergence of order p=m+2 on a certain finite subset of I (while the global convergence order is m+1; this subset does not contain the knots ZN. In this note it will be shown that superconvergence on ZN can be attained only if some of the collocation points coalesce (Hermite-type collocation). © 1979 Springer-Verlag.