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.
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
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
