Symmetric Runge-Kutta Methods with Higher Derivatives and Quadratic Extrapolation

  • Gennady Yu. Kulikov
  • Ekaterina Yu. Khrustaleva
  • Arkadi I. Merkulov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


In this paper we study the symmetry of Runge-Kutta methods with higher derivatives. We find conditions which provide this property for the above numerical methods. We prove that the family of E-methods constructed earlier consists of symmetric methods only, which lead to the quadratic extrapolation technique in practice.


Adjoint Method Symmetric Method Underlying Method Hermite Type Increment Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gennady Yu. Kulikov
    • 1
  • Ekaterina Yu. Khrustaleva
    • 2
  • Arkadi I. Merkulov
    • 2
  1. 1.School of Computational and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  2. 2.Ulyanovsk State UniversityUlyanovskRussia

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