An application of the fundamental spline-functions of an odd degree to an approximate solution of integral equations (Q1123575)

Polynomial splines of odd degree are used to furnish approximate solutions of an inhomogeneous Fredholm integral equation of the second kind defined on a finite interval. The fundamental splines satisfy what the author calls ``symmetric boundary conditions'' in some neighbourhood of the end points of the interval. A linear combination of these splines is taken to approximate the exact solution at the knots. It is shown that the approximate solution converges to the solution of the equation as the maximum spacing of the knots decreases to zero. Estimates are given for the orders of convergence of the solution and its derivatives to those of the true solution. There are no numerical examples.