ON THE CONVERGENCE ANALYSIS OF THE SPLINE COLLOCATION METHOD FOR SYSTEM OF INTEGRAL ALGEBRAIC EQUATIONS OF INDEX-2

Abstract

This article presents some theoretical results for polynomial spline collocation solution to a new class of semi-explicit Integral Algebraic Equations (IAEs) of index-2, which has been introduced in a recent paper of the authors (Hadizadeh, M., Ghoreishi, F. and Pishbin, S. [2011] "Jacobi spectral solution for integral-algebraic equations of index-2, " Appl. Numer. Math.61, 131–148). Critical issues for numerical analysis of the spline collocation method for this type of Volterra systems are discussed and the necessary and sufficient conditions are presented which guarantee the convergence of the method. We analyze the rate of convergence for two disjoint cases of collocation parameter cm. Numerical results confirm the rate of decay of the error predicted by this theory.