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Runge-Kutta Methods with Equation Dependent Coefficients

  • L. Gr. Ixaru
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

The simplest two and three stage explicit Runge-Kutta methods are examined by a conveniently adapted form of the exponential fitting approach. The unusual feature is that the coefficients of the new versions are no longer constant, as in standard versions, but depend on the equation to be solved. Some valuable properties emerge from this. Thus, in the case of three-stage versions, although in general the order is three, that is the same as for the standard method, this is easily increased to four by a suitable choice of the position of the stage abscissas. Also, the stability properties are massively enhanced. Two particular versions of order four are A-stable, a fact which is quite unusual for explicit methods. This recommends them as efficient tools for solving stiff differential equations.

Keywords

Runge-Kutta method Exponential fitting A-stability 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • L. Gr. Ixaru
    • 1
    • 2
  1. 1.Department of Theoretical Physics“Horia Hulubei” National Institute of Physics and Nuclear EngineeringBucharestRomania
  2. 2.Academy of Romanian ScientistsBucharestRomania

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