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Stepsize Selection in Explicit Runge-Kutta Methods for Moderately Stiff Problems

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DOI: 10.4236/am.2011.26094    7,596 Downloads   13,200 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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[6] R. L. Burden and J. D. Faires, “Numerical Analysis,” 9th Edition, Brooks/Cole, Pacific Grove, 2011.

  
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