Integratzaile simetrikodun 10 ordenako konposizio metodo simetrikoen bilaketa

Abstract

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they can be used to increase the order of accuracy of a given basic numerical integration scheme. We will focus on symmetric
composition methods involving some basic second order symmetric integrator with different step sizes. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients 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 integrators of s = 31 stages are explored.