Modified Extended BDF Time-Integration Methods, Applied to Circuit Equations

  • Sandra Allaart-Bruin
  • Jan ter Maten
  • Sjoerd Verduyn Lunel
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 4)


Electric circuits designers are frequently interested in the transient behaviour of the designed circuit. A common method for time integration of the Differential Algebraic circuit Equations (DAE) is the Backward Differentiation Formula (BDF) method. In 1983, J. Cash proposed the Modified Extended BDF (MEBDF) method, which combines better stability properties and higher order of convergence than BDF, but requires more computations per step. We prove reduction of convergence order for MEBDF when applied to DAE’s with higher DAE-index. However, because in practice, in circuit analysis, the DAE-index does not exceed 2, the reduction is quite moderate and it equals the BDF-order in that case. One gains better, or even unconditional, stability. One also obtains consistent solutions.


Consistent Solution Inverse Function Theorem Initial Valu Backward Differentiation Formula Algebraic Part 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sandra Allaart-Bruin
    • 1
  • Jan ter Maten
    • 1
  • Sjoerd Verduyn Lunel
    • 2
  1. 1.Philips Research LaboratoriesEindhoven University of TechnologyEindhoven
  2. 2.Leiden UniversityLeiden

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