On the estimation of errors propagated in the numerical integration of ordinary differential equations

Summary In this paper we describe a method for the estimation of global errors. An heuristic condition of validity of the method is given and several applications are described in detail for problems of ordinary differential equations with either initial or two point boundary conditions solved by finite difference formulas. The main idea of the method can be extended to other type of problems and applications to a problem solved by spline functions and to some partial differential equations solved by finite differences methods are outlined.Some results of the present work have been reported at the Conference on the Numerical Solution of Differential Equations, held at the University of Dundee, Scotland in 1973