Application of Spline Functions to Systems of Volterra Integral Equations of the First and Second Kinds

摘要

Continuous approximations to the solution of systems of Volterra integral equations of the first and second kinds are sought by methods using spline functions of degreem, deficiency-(k—1), i.e. inCm—k, and a fixed quadrature rule of degreep-1,p≥m-1. The resulting method is called an (m, k)-method. The stability behaviour of the (m, 1)- and the (m, m)-method is studied for arbitrarily finitem. Also studied is the stability of the (m, m-1)-method for second-kind systems. Convergence results and asymptotic formulae for the discretization error are obt