Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
The Bruun Rule tests of the theory and concluded that "the concept henceforth be known as "Bruun's Rule."""" Per Bruun has since published works to clarify the limitations and practicality of his model, including "Review of Conditions for Uses of the Bruun Rule of Erosion" in 1983, and "The Bruun Rule of Erosion by Sea-Level Rise: A Discussion on Large-Scale Two- and Three- Dimensional Usages" in 1988. These publications outline the rule's limitations and practicality and stress that, though this model is intentionally two dimensional, it is applied to three dimensional environments in practice. Bruun states that the rule "must be subjected to