clarke@csri.toronto.edu (Jim Clarke) (03/16/89)
!!!!!!!!!!!!!!! CHANGE IN DATE, TIME AND PLACE:
NUMERICAL ANALYSIS SEMINAR - Wednesday, March 29, 3:10 p.m. in Room GB 248
(GB = Galbraith Building, 35 St. George Street)
Paul Muir
Saint Mary's University
"Error Expressing for
Reflected and Averaged Implicit Runge-Kutta Methods"
In addition to their usefulness in the numerical solution of ini-
tial value ODE's, the implicit Runge-Kutta (IRK) methods are also
important for the solution of two-point boundary value problems.
Recently, several classes of modified IRK methods which improve
significantly on the efficiency of the standard IRK methods in
this application have been presented. One such class is the Aver-
aged IRK methods; a member of the class is obtained by applying
an averaging operation to a non-symmetric IRK method and its re-
flection. In this talk we investigate the forms of the error ex-
pressions for reflected and averaged IRK methods. Our first
result relates the expression for the local error of the reflect-
ed method to that of the original method. Our main result relates
the error expression of an averaged method to that of the method
upon which it is based. We apply these results to show that for
each member of the class of the averaged methods, there exists an
embedded lower order method suitable for use in error estimation,
in a formula-pair fashion.
--
Jim Clarke -- Dept. of Computer Science, Univ. of Toronto, Canada M5S 1A4
(416) 978-4058
clarke@csri.toronto.edu or clarke@csri.utoronto.ca
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