AdaptiveIntegrator2D Class

public class AdaptiveIntegrator2D : NumericalIntegrator2D

Public Class AdaptiveIntegrator2D
	Inherits NumericalIntegrator2D

public ref class AdaptiveIntegrator2D : public NumericalIntegrator2D

type AdaptiveIntegrator2D = 
    class
        inherit NumericalIntegrator2D
    end

Inheritance

Object  →  ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>>  →  ManagedIterativeAlgorithm<Double>  →  IterativeAlgorithm  →  NumericalIntegrator2D  →  AdaptiveIntegrator2D

Use the AdaptiveIntegrator2D class to compute integrals of functions with two variables over rectangular areas. This class uses an adaptive algorithm and in most cases far outperforms alternative methods.

AdaptiveIntegrator2D inherits from NumericalIntegrator2D, the abstract base class for all classes that implement numerical integration in two 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 function of two variables delegate 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 integration rule to use to approximate integrals on a subregion. For oscillating target functions, the higher order rules will tend to give better results.

Several enhancements make this the integration algorithm of choice, especially for 'difficult' target functions.

Reference