Derivation of Explicit Difference Schemes for Ordinary Differential Equations with the Aid of Lagrange–Burmann Expansions

  • Evgenii V. Vorozhtsov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)


We propose to derive the explicit multistage methods of the Runge–Kutta type for ordinary differential equations (ODEs) with the aid of the expansion of grid functions into the Lagrange–Burmann series. New explicit first- and second-order methods are derived, which are applied to the numerical integration of the Cauchy problem for a moderately stiff ODE system. It turns out that the L 2 norm of the error of the solution obtained by the new numerical second-order method is 50 times smaller than in the case of the classical second-order Runge–Kutta method.


Local Error Kutta Method Absolute Stability Explicit Method Negative Real Axis 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Evgenii V. Vorozhtsov
    • 1
  1. 1.Khristianovich Institute of Theoretical and Applied MechanicsRussian Academy of SciencesNovosibirskRussia

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