A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs

  • Authors:

  • J. Javier Ibáñez;Vicente Hernández;Pedro A. Ruiz;Enrique Arias

  • Affiliations:

  • Instituto de Instrumentación en Imagen Molecular (I3M), Universidad Politécnica Valencia, Camino de Vera s/n, 46022-Valencia, Spain;Instituto de Instrumentación en Imagen Molecular (I3M), Universidad Politécnica Valencia, Camino de Vera s/n, 46022-Valencia, Spain;Instituto de Instrumentación en Imagen Molecular (I3M), Universidad Politécnica Valencia, Camino de Vera s/n, 46022-Valencia, Spain;Albacete Research Institute of Informatics, University of Castilla-La Mancha, Avda. España s/n, 02071-Albacete, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2011

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Abstract

Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Pade approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems.