11 citations · 16 across the 7 of their papers we have counts for
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Linear multistep methods with repeated global Richardson extrapolation
Imre Fekete, Lajos Lóczi
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear mult…
Linear multistep methods and global Richardson extrapolation
Imre Fekete, Lajos Lóczi
In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMM…
Positivity preservation of implicit discretizations of the advection equation
Yiannis Hadjimichael, David I. Ketcheson, Lajos Lóczi
We analyze, from the viewpoint of positivity preservation, certain discretizations of a fundamental partial differential equation, the one-dimensional advection equation with perio…
On the definition of the stability region of multistep methods
Lajos Lóczi
The usual definition of the stability region of implicit multistep methods often implies that there are some isolated points of stability within the region of instability of the nu…
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…
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…