AdaptiveIntegratorND Class

Use the AdaptiveIntegratorND to compute integrals of functions with one or more variables over box shaped regions. This class uses an adaptive algorithm and in most cases far outperforms alternative methods.

AdaptiveIntegratorND inherits from NumericalIntegratorND, the abstractMustInheritabstractabstract (MustInherit in Visual Basic) base class for all classes that implement numerical integration in multiple dimensions. It, in turn, inherits from the IterativeAlgorithm class. All properties of this class are also available. The AbsoluteTolerance and RelativeTolerance properties set the desired precision as specified by the ConvergenceCriterion property. The default value for both tolerances is SqrtEpsilon (roughly 10^-8). MaxIterations sets the maximum number of iterations, which in this case is the maximum number of subregions. The default value for this property is 5000. IterationsNeeded returns the actual number of iterations performed after the algorithm has completed.

The Integrate()()()() method does the actual work of numerically integrating an integrand. It takes three parameters. The first parameter is a delegate that represents a multivariate function that specifies the function to integrate. The second and third parameters are Double values that specify the lower and upper bounds of the integration region in the X direction. The fourth and fifth parameters are Double values that specify the lower and upper bounds of the integration region in the Y direction.

The IntegrationRule property lets you specify which Gauss-Kronrod integration rule to use to approximate integrals on a subinterval. The default is the 31-point rule for normal integrands, and the 15-point rule when singularities are expected, and when integrating over infinite intervals. For oscillating target functions, the higher order rules will tend to give better results.