<Li> k 4 (\ displaystyle k_ (4)) is the increment based on the slope at the end of the interval, using y + h k 3 (\ displaystyle y + hk_ (3)). </Li> <P> In averaging the four increments, greater weight is given to the increments at the midpoint . If f (\ displaystyle f) is independent of y (\ displaystyle y), so that the differential equation is equivalent to a simple integral, then RK4 is Simpson's rule . </P> <P> The RK4 method is a fourth - order method, meaning that the local truncation error is on the order of O (h 5) (\ displaystyle O (h ^ (5))), while the total accumulated error is on the order of O (h 4) (\ displaystyle O (h ^ (4))). </P> <P> The family of explicit Runge--Kutta methods is a generalization of the RK4 method mentioned above . It is given by </P>

Error in 4th order runge kutta method is of the order of
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