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A modified Runge-Kutta method

Hybrid Computer Laboratory The University of Wisconsin Madison, Wisconsin

It is possible to replace k₂ in a 4th-order Runge-Kutta for mula (also Nth-order 3 N 5) by a linear combination of k₁ and the k_i's in the last step, using the same procedure for computing the other k_i's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values.

Experimental results are shown in verification of the for mula.

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