Applying root-finding techniques to extend Quantized-State-Systems-based Solvers

ERIC BIAGIOLI; LUIS PEÑARANDA; FEDERICO BERGERO; ROBERTO IMBUZEIRO OLIVEIRA

Valparaíso

Conferencia; CLEI 2016; 2016

In this work we propose the usage of root isolationalgorithms to extend Quantized-State-Systems-based methods forintegrating systems of Ordinary Differential Equations to higherorders. In its inner loop QSS methods of order n need to computethe minimum positive root of a n-degree polynomial. The lackof analytical expressions for the roots of polynomial of degreegreater than four limits the QSS methods to fourth order orless. We make an observation which, combined with the usageof root-finding techniques, allows the generalization to QSS ofany order. Moreover, we show experimentally that, consideringour algorithmic improvements, higher order methods do requireconsiderably fewer iterations than lower order ones.