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E. Hairer and G. Wanner, “Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems,” Springer, Berlin, 2000.

has been cited by the following article:

• 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.