High Quality Content by WIKIPEDIA articles! Adaptive Simpson's method, also called adaptive Simpson's rule, is a method of numerical integration proposed by William M. McKeeman in 1962. It is perhaps the first adaptive algorithm for numerical integration to appear in print, although more modern adaptive methods based on Gauss–Kronrod quadrature and Clenshaw–Curtis quadrature are now generally preferred. Adaptive Simpson's method uses an estimate of the error we get from calculating a definite integral using Simpson's rule. If the error exceeds a user-specified tolerance, the algorithm calls for subdividing the interval of integration in two and applying adaptive Simpson's method to each subinterval in a recursive manner. The technique is usually much more efficient than composite Simpson's rule since it uses fewer function evaluations in places where the function is well-approximated by a quadratic function.

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