Integrator

A List of mathematical integrators: Romberg integrator, Composite trapezoid rule, Composite midpoint rule, Composite Three-point Gaussian, Composite Simpson 1/3 rule

github: kwyip

Romberg integrator

Code: romberg.m

It produces a matrix r of size (n+1,n+1). The entry of r(n+1,n+1) contains accurate solution.

Composite Trapezoid rule over n intervals, (for just trapezoid, put n = 1)

Code: compositetrapezoid.m

Composite Midpoint rule over n intervals, (for just Midpoint, put n = 1)

Code: compositemidpoint.m

Composite Three-point Gaussian over n intervals (for just Three-point Gaussian, put n = 1)

Code: composite3pointgaussian.m

Composite Simpson's 1/3 rule over n intervals (for just Simpson's 1/3 rule, put n = 1)

Code: compositesimpson13.m

Example: testing for composite rules for integrating from 0 to 2pi over 32 intervals

Code: exampletesting32intervals.m

Output:

A colored plot of the function that needs to be integrated: