Adaptive Integration of Stiff ODE

Article type: Research Article

Authors: Čiegis, Raimondas | Suboč, Olga | Čiegis, Remigijus

Affiliations: Vilnius Gediminas Technical University, Saulėtekio 11, 2054 Vilnius, Lithuania. E-mail: rc@fm.vtu.lt | Kaunas Faculty of Humanities Vilnius University, Muitinės 8, 3000 Kaunas, Lithuania. E-mail: remigijus.ciegis@aula.vukhf.lt

Abstract: The accuracy of adaptive integration algorithms for solving stiff ODE is investigated. The analysis is done by comparing the discrete and exact amplification factors of the equations. It is proved that the usage of stiffness number of the Jacobian matrix is sufficient in order to estimate the complexity of solving ODE problems by explicit integration algorithms. The complexity of implicit integration algorithms depends on the distribution of eigenvalues of the Jacobian. Results of numerical experiments are presented.

Keywords: stiff ODE, adaptive integration, explicit and implicit algorithms

DOI: 10.3233/INF-2000-11402

Journal: Informatica, vol. 11, no. 4, pp. 371-380, 2000