Adaptive Integration Methods

Adaptive integration methods are numerical techniques used to approximate definite integrals of functions by dynamically adjusting the integration intervals or the number of nodes based on the local properties of the function. These methods aim to achieve a specified level of accuracy while minimizing the number of function evaluations.

Adaptive integration methods can be applied to various numerical integration techniques, such as the trapezoidal rule, Simpson’s rule, or Gaussian quadrature. They are particularly useful for functions with rapidly varying or discontinuous derivatives, as they can focus computational effort on regions with the highest error.