Convergence properties of the quadratic iterated splines method for functional third order two-point boundary value problems

Abstract The purpose of this work is to construct a Green’s function iterated splines method which is the simplest one from computational complexity point of view and ensures the maximal order of convergence, for solving third order two-point boundary value problems with deviating argument. The Picard-Green’s method is combined with a quadratic spline interpolation procedure, and choosing a suitable quadrature rule, we prove that the order of convergence is 3. Some remarks concerning the application of the same method to initial value problems and Volterra integral equations with deviating argument are pointed out. In the last section, several numerical experiments are presented in order to illustrate the performances of this method and to test the obtained theoretical results.