This algorithm can be modified to an "adaptive" form by increasing the step size when the error is too small and decreasing it when it is too large, leading the error to oscillate about the optimum value.
This algorithm can be modified to an "adaptive" form by increasing the step size when the error is too small and decreasing it when it is too large, leading the error to oscillate about the optimum value. The local truncation error for this algorithm is proportional to the interval being used raised to the power of one plus the order of the algorithm. The most common form of this algorithm is its fourth-order variant, in which doubling the number of steps leads to a 16-fold reduction in error. This algorithm improves on the Taylor algorithm by not having to compute derivatives, and it begins with a calculation identical to the Euler method. This algorithm's fourth-order variant proceeds by computing the weighted average of four slopes, with values interior to a partition interval weighted twice as heavily as the edge values, using symmetrization to cancel out lower order error terms. For 10 points, identify this algorithm for numerically integrating ordinary differential equations, named for its two German formulators.
This algorithm can be modified to an "adaptive" form by increasing the step size when the error is too small and decreasing it when it is too large, leading the error to oscillate about the optimum value.
Runge-Kutta method