Integratzaile simetrikodun 10 ordenako konposizio metodo simetrikoen bilaketa

Abstract

Composition methods are useful when solving Ordinary Differential Equa-tions (ODEs) as they can be used to increase the order of accuracy of a given basic nu-merical integration scheme. We will focus on symmetric composition methods involv-ing some basic second order symmetric integrator with different step sizes. The introduction of symmetries into these methods simplifies the order conditions and re-duces the number of unknowns. Several authors have worked in the search of the coef-ficients of these type of methods: the best method of order 8 has 17 stages, 10-order methods of 31, 33 and 35 stages have been also found. In this work two techniques that we have built to obtain 10-order symmetric composition methods of symmetric inte-grators of s = 31 stages are explored.