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math.NA2013
On the absolute stability regions corresponding to partial sums of the exponential function
David Ketcheson, Tihamér A. Kocsis, Lajos Lóczi
Certain numerical methods for initial value problems have as stability function the nth partial sum of the exponential function. We study the stability region, i.e., the set in the…
math.NA2013★ 11 cited
Propagation of internal errors in explicit Runge--Kutta methods and internal stability of SSP and extrapolation methods
David I. Ketcheson, Lajos Lóczi, Matteo Parsani
In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example…