Cattmul-Rom spline approach and the order of convergence of Green’s functional method for functional differential equations

The purpose of this work is to investigate the convergence properties Green’s function method applied boundary value problems for functional differential equations. Recently, involving Picard and Mann iterations, a technique was developed (in Int. J. Computer Math. 95, no. 10 (2018) 1937-1949) third order equations, but without specifying proposed method. In improve aspect, here we establish maximal two-point associated second context, by using suitable quadrature rule appropriate spline interpolation procedure, iterations are approximated sequence cubic splines on uniform mesh. Some numerical experiments presented in test theoretical results illustrate accuracy