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

DOI: 10.4236/am.2011.26094, PP. 711-717

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

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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.

References

[1]  J. C. Butcher, “Numerical Methods for Ordinary Differential Equations,” Wiley, Chichester, 2003. doi:10.1002/0470868279
[2]  E. Fehlberg, “Low-Order Classical Runge-Kutta Formulas with Step Size Control and Their Application to Some Heat Transfer Problems,” Computing, Vol. 6, 1970, pp. 61-71. doi:10.1007/BF02241732
[3]  L. F. Shampine and M. W. Reichelt, “The MATLAB ODE Suite,” SIAM Journal on Scientific Computing, Vol. 18, No. 1, 1970, pp. 1-22. doi:10.1137/S1064827594276424
[4]  D. Kincaid and W. Cheney, “Numerical Analysis: Mathematics of Scientific Computing,” 3rd Edition, Brooks/Cole, Pacific Grove, 2002.
[5]  E. Hairer and G. Wanner, “Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems,” Springer, Berlin, 2000.
[6]  R. L. Burden and J. D. Faires, “Numerical Analysis,” 9th Edition, Brooks/Cole, Pacific Grove, 2011.

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