Not classic difference schemes for ordinary differential equations of the second order(initial value problems)

M. V. Bulatov^a, T. V. Amocova^b, G. Vanden Berge<sup>c

a</sup> Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk
^b East Siberian State Academy of Education, Irkutsk
^c Ghent University

Abstract: In this paper we consider the initial problem for systems of linear ordinary differential equations of second order which do not content the first derivative. To solve such problems numerically, we propose new two-step difference schemes of order 4-th. We give a thorough analysis of the schemes proposed, compare them with well-known ones, and test them on modal examples.

Keywords: ordinary differential equations of second order, initial value problems, difference schemes, Numerov method.

UDC: 517.9

Received: 22.06.2011