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IMA Journal of Numerical Analysis Advance Access published online on May 19, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn086
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Trees, B-series and exponential integrators

J. C. Butcher{dagger}

Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1011, New Zealand

{dagger} Email: butcher{at}math.auckland.ac.nz

Received on 1 May 2008. Revised on 26 November 2008.


  Abstract

Questions concerning the accuracy of numerical methods for differential equations are often analysed using B-series and other formulations based on rooted trees. The analysis of numerical methods, such as Rosenbrock and certain exponential methods, requires an additional algebraic structure to represent the direct use of Jacobian matrices in the computation. It is shown how this can be done within a context containing a broad review of the existing B-series formulation.

Key Words: B-series; Runge–Kutta group; Runge–Kutta methods; Rosenbrock methods; exponential integrators

Dedicated to the memory of A. R. Mitchell, 1921–2007.


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