TrapezoidIntegrator Class

public sealed class TrapezoidIntegrator : NumericalIntegrator

Public NotInheritable Class TrapezoidIntegrator
	Inherits NumericalIntegrator

public ref class TrapezoidIntegrator sealed : public NumericalIntegrator

[<SealedAttribute>]
type TrapezoidIntegrator = 
    class
        inherit NumericalIntegrator
    end

Inheritance

Object  →  ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>>  →  IterativeAlgorithm<Double>  →  NumericalIntegrator  →  TrapezoidIntegrator

The classic trapezoid rule is one of the simplest numerical integration algorithms around. The interval is divided into smaller subintervals. On each subinterval, the function is approximated by a straight line.

This algorithm is of order 1. In each iteration, the number of points is doubled. The difference between successive approximations is taken as the estimate for the integration error.

Because the order of the algorithm is so low, use of this algorithm is not generally recommended for general use. It does provide a unique feature in that can produce absolute bounds on the value of the integral of some functions. It produces a lower bound for concave integrands, and an upper bound for convex integrands. Complementary bounds are produced by the MidpointIntegrator.

Reference