Diagonally Implicit RK Methods

  • Ernst Hairer
  • Gerhard Wanner
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 14)

Abstract

We continue to quote from this nice paper: “To integrate a system of n differential equations, an implicit method with a full s × s matrix requires the solution of ns simultaneous implicit (in general nonlinear) equations in each time step (...) One way to circumvent this difficulty is to use a lower triangular matrix (a ij )(i.e., a matrix with a ij = 0 for i < j); the equations may then be solved in s successive stages with only an n -dimensional system to be solved at each stage”. In accordance with many authors, and in disaccordance with others (see above), we call such a method diagonally implicit (DIRK).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Ernst Hairer
    • 1
  • Gerhard Wanner
    • 1
  1. 1.Section de Mathématiques, C.P. 240Université de GenèveGenève 24Switzerland

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