Second derivative Runge-Kutta collocation methods based on Lobatto nodes for stiff systems

Second derivative Runge-Kutta collocation methods for the numerical solution of sti system of rst order initial value problems in ordinary dierential equations are derived and studied. The inclusion of the second derivative terms enabled us to derive a set of methods which are convergent with large...

Full description

Saved in:
Bibliographic Details
Published inJournal of Modern Methods in Numerical Mathematics Vol. 8; no. 1-2; p. 118
Main Authors Yakubu, G. D., Kumleng, G. M., Markus, S.
Format Journal Article
LanguageEnglish
Published 15.10.2017
Online AccessGet full text

Cover

More Information
Summary:Second derivative Runge-Kutta collocation methods for the numerical solution of sti system of rst order initial value problems in ordinary dierential equations are derived and studied. The inclusion of the second derivative terms enabled us to derive a set of methods which are convergent with large regions of absolute stability. Although the implementation of the methods remains iterative in a precisely dened way, the advantage gained makes them suitable for solving sti system of equations with large Lipschitz constants. The derived methods are illustrated by the applications to some test problems of sti system found in the literature and the numerical results obtained conrm the potential of the second derivative methods.
ISSN:2090-8296
2090-4770
DOI:10.20454/jmmnm.2017.1349