Romberg

Performs Romberg integration

Call Romberg.m to perform Romberg integration with specified tolerance and gives results

Call RombergDisp.m to display Romberg integration scheme coefficients

Icon image: An Introduction to Numerical Methods and Analysis, 2nd Edition

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [I] = Romberg(func,a,b,tol,kmax)

Romberg integrates function "func" of one variable and nonsingular

from "a" to "b" with tolerance "tol" and maximum order of "kmax".

0 < tol < 1 & kmax > 0. Using Romberg integration.

I = Romberg(@func,a,b,tol,kmax)

I = Romberg(@func,a,b,tol)ss,ssdefault kmax = 15

I = Romberg(@func,a,b)ss,ssdefault tol = 1e-10ss,ssdefault kmax = 15

e.g.

I = Romberg(@sin,0,pi)

I = 2.000000000000000

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [] = RombergDisp(func,a,b,k)

Romberg integrates function "func" of one variable and nonsingular

from "a" to "b" with order of "k" and displays all results.

k >= 0. Using Romberg integration.

I = RombergDisp(@func,a,b,k)

e.g.

RombergDisp(@sin,0,pi,2)

0.000000000000000ss

1.570796326794897ss2.094395102393195ss

1.896118897937040ss2.004559754984421ss1.998570731823836