BIT Numerical Mathematics

, Volume 43, Issue 3, pp 467-483

First online:

Modified Implicit–Explicit BDF Methods for Nonlinear Parabolic Equations

  • Georgios AkrivisAffiliated withComputer Science Department, University of Ioannina
  • , Fotini KarakatsaniAffiliated withMathematics Department, University of Crete

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Implicit–explicit multistep methods for nonlinear parabolic equations were recently analyzed. If the implicit scheme is one of the backward differentiation formulae (BDF) of order up to six, then the corresponding implicit–explicit method of the same order is stable provided the stability constant is less than a specific scheme-dependent constant. Based on BDF, implicit methods are constructed such that the corresponding implicit–explicit scheme of the same order exhibits improved stability properties.

implicit–explicit multistep schemes nonlinear parabolic equations backward differentiation formulae