Abstract
A Runge-Kutta algorithm for an nth order initial value problem (IVP) is developed by means of simple modifications of the algorithm used for the first-order IVP. Auxiliary state variables are used to convert the nth order IVP into a system of first-order IVPs. Consequently, the corresponding computer program for the nth order is developed by modification of the program used for the first-order IVP in a suitable fashion. It is shown that the method is straightforward and its computer program is extremely compact. For illustration, the program is applied to a fourth-order IVP involving nonlinear terms.
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