Malaysian Journal of Mathematical Sciences, September 2018, Vol. 12, No. 3
Theoretical Analysis of Symmetric Runge-Kutta Methods
Gorgey, A.
Corresponding Email: annie_gorgey@fsmt.upsi.edu.my
Received date: 16 December 2017
Accepted date: 14 August 2018
Abstract:
This article give the theoretical analysis for some symmetric Runge-Kutta methods such as the 2-stage Gauss, 3-stage Gauss, 3-stage Lobatto IIIA and 4-stage Lobatto IIIA methods. The theoretical analysis on the asymptotic error expansions by the 2-stage Gauss (G2) and 3-
stage Lobatto IIIA (L4) methods are studied in detailed for the Prothero-Robinson (PR) problem. For the 3-stage Gauss (G3) and 4-stage Lobatto IIIA (L4) methods, the behavior of these methods are studied numerical and theoretically for PR problem. It is observed that G3 and L4 gives oscillatory error behavior when applied to the PR problem. However, these numerical results are shown to be improved by the symmetrizer.
Keywords: Asymptotic error expansions, symmetric, smoothing, symmetrizer, extrapolation
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