by I. P. Gavrilyuk, M. Hermann, M. V. and Makarov Kutniv
Preprint series: 05-15, Reports on Numerical Mathematics
I. P. Gavrilyuk, M. Hermann, M. V. and Makarov Kutniv
Abstract: Two-point boundary value problems for a system of nonlinear first order ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which possesses a prescribed order of accuracy O(|h|^m) w.r.t. the maximal step size |h|. This m-TDS represents a system of nonlinear algebraic equations for the approximate values of the exact solution on the grid. In the present paper new efficient methods for the implementation of a m-TDS are discussed. Examples are given which illustrate the theorems proved in this paper.
Keywords: systems of nonlinear ordinary differential equations, nonlinear boundary-value problem, two-point difference scheme, exact difference scheme, truncated two-point difference scheme of an arbitrary given accuracy order, and fixed point iteration