Experiments with a variable-stepsize/variable-order code based on explicit general linear methods
Ali Abdi (University of Tabriz), Zdzislaw Jackiewicz
This talk is about various issues relevant to the development of the
code for nonstiff ordinary differential systems based on a class of
general linear methods (GLMs) with inherent Runge–Kutta stability
(IRKS). These issues include the choice of initial stepsize, computation
of the starting vector, construction of continuous interpolants, local
error estimation, stepsize and order changing strategies, and updating
vectors of external approximations, which propagate from step to step.
The resulting experimental code irks14.m based on GLMs with
IRKS of order \(1\leq p\leq4\) is
tested and compared with the state-of-art code from the Matlab ODE suite for the numerical solution of
nonstiff ODEs, and it is demonstrated that irks14.m is more
efficient than ode45.m for moderate and stringent
tolerances.
Keywords: Ordinary differential equations, General linear methods, Inherent Runge–Kutta stability, Adaptive stepsize and order selection.