Blended implicit methods for the numerical solution of DAE problems

  • Authors:

  • Luigi Brugnano;Cecilia Magherini;Filippo Mugnai

  • Affiliations:

  • Dipartimento di Matematica "U. Dini", Viale Morgagni 67/A, 50134 Firenze, Italy;Dipartimento di Matematica "U. Dini", Viale Morgagni 67/A, 50134 Firenze, Italy;Dipartimento di Matematica "U. Dini", Viale Morgagni 67/A, 50134 Firenze, Italy

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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Abstract

Recently, a new approach for solving the discrete problems, generated by the application of block implicit methods for the numerical solution of initial value problems for ODEs, has been devised [L. Brugnano, Blended block BVMs (B"3VMs): a family of economical implicit methods for ODEs, J. Comput. Appl. Math. 116 (2000) 41-62; L. Brugnano, C. Magherini, Blended implementation of block implicit methods for ODEs, Appl. Numer. Math. 42 (2002) 29-45; L. Brugnano, D. Trigiante, Block implicit methods for ODEs, in: D. Trigiante (Ed.), Recent Trends in Numerical Analysis, Nova Science Publishers, New York, 2001, pp. 81-105]. This approach is based on the so-called blended implementation of the methods, giving corresponding blended implicit methods. The latter have been implemented in the computational code BiM [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164-165 (2004) 145-158]. Blended implicit methods are here extended to handle the numerical solution of DAE problems, resulting in a straightforward generalization of the basic approach.