SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Deferred correction based on exponentially fitted mono-implicit Runge-Kutta methods

M.V. Daele and D. Hollevoet

Deferred correction [1] is a well-known approach to the numerical solution of general first order systems of nonlinear two-point boundary value problems. A well-known code built on this technique is TWPBVP. The idea behind (iterated) deferred correction is to (iteratively) correct for the smooth errors of the discretization algorithm. This is also the original idea behind exponential fitting methods. Exponential fitting [2] is a procedure that produces variants of classical methods, aimed to solve problems with exponential (or in the complex case oscillating) solutions more efficiently. In this talk, the combination of exponential fitting and deferred correction based on mono-implicit Runge-Kutta methods is discussed. Particular attention is given to the parameter selection of the exponentially fitted deferred correction schemes to annihilate or minimize the leading error term. Several algorithms are discussed and illustrated with numerical results.

[1] J.R. Cash, Z.Bashir-Ali and H.H.M. Silva, Lobatto deferred correction for stiff two-point boundary value problems, CAMWA 36 (1998) 59-69.
[2] G. Ixaru and G. Vanden Berghe, Exponential fitting, Kluwer Academic Publishers, Dordrecht, 2004.

Organized by         Universidad de Valladolid     IMUVA