This VI compares the difference between the 4-points and 7-points Lobatto quadratures on the interval with tolerance to terminate the calculation iteration. If the difference is less than the tolerance, the algorithm stops the iteration and moves on to next interval.

1D Quadrature

This VI numerically evaluates the following integral using the adaptive Lobatto quadrature:

where x₁ is the upper limit and x₀ is the lower limit.

To obtain high accuracy, this VI divides an interval into subintervals when the integrand f(x) varies sharply, as shown in the following front panel.

2D Quadrature

This VI numerically evaluates the following integral using the adaptive Lobatto quadrature:

where x₁ is x upper limit, x₀ is x lower limit, y₁ is y upper limit, and y₀ is y lower limit.

The 2D Quadrature instances divide an interval block into many sub-blocks when the integrand f(x,y) varies sharply.

3D Quadrature

This VI numerically evaluates the following integral using the adaptive Lobatto quadrature:

where x₁ is x upper limit, x₀ is x lower limit, y₁ is y upper limit, y₀ is y lower limit, z₁ is z upper limit, z₀ is z lower limit.

The 3D Quadrature instances divide an interval cube into many sub-cubes when the integrand f(x,y,z) varies sharply.

Examples

Refer to the following example files included with LabVIEW.

• labview\examples\Mathematics\Integration and Differentiation\VI Reference Based Quadrature.vi