TITLE:
Stepsize Selection in Explicit Runge-Kutta Methods for Moderately Stiff Problems
AUTHORS:
Justin Steven Calder Prentice
KEYWORDS:
Moderately Stiff Problems, Runge-Kutta, Stepsize, Jacobian, Stability Region
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.6,
June
21,
2011
ABSTRACT: We present an algorithm for determining the stepsize in an explicit Runge-Kutta method that is suitable when solving moderately stiff differential equations. The algorithm has a geometric character, and is based on a pair of semicircles that enclose the boundary of the stability region in the left half of the complex plane. The algorithm includes an error control device. We describe a vectorized form of the algorithm, and present a corresponding MATLAB code. Numerical examples for Runge-Kutta methods of third and fourth order demonstrate the properties and capabilities of the algorithm.