Spline Collocation for Volterra - Fredholm Integro-Differential Equations

Abstract

A collocation procedure is developed for the linear and nonlinear Volterra - Fredholm integrodifferential equations, using the globally defined B-spline and auxiliary basis functions. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of the proposed numerical method is studied theoretically.