Author(s)

Justin Steven Calder Prentice

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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.

Moderately Stiff Problems, Runge-Kutta, Stepsize, Jacobian, Stability Region

J. Prentice, "Stepsize Selection in Explicit Runge-Kutta Methods for Moderately Stiff Problems," Applied Mathematics, Vol. 2 No. 6, 2011, pp. 711-717. doi: 10.4236/am.2011.26094.