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Highlights from
Numerical Methods Using MATLAB, 3e

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Numerical Methods Using MATLAB, 3e

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20 Aug 2002 (Updated )

Companion Software

[R,quad,err,h]=romber(f,a,b,n,tol)
function [R,quad,err,h]=romber(f,a,b,n,tol)

%Input  - f is the integrand input as a string 'f'
%       - a and b are upper and lower limits of integration
%       - n is the maximum number of rows in the table
%       - tol is the tolerance
%Output - R is the Romberg table
%       - quad is the quadrature value
%       - err is the error estimate
%       - h is the smallest step size used

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.
%Upper Saddle River, NJ 07458

M=1;
h=b-a;
err=1;
J=0;
R=zeros(4,4);
R(1,1)=h*(feval(f,a)+feval(f,b))/2;

while((err>tol)&(J<n))|(J<4)
   J=J+1;
   h=h/2;
   s=0;
   for p=1:M
      x=a+h*(2*p-1);
      s=s+feval(f,x);
   end
   R(J+1,1)=R(J,1)/2+h*s;
   M=2*M;
   for K=1:J
      R(J+1,K+1)=R(J+1,K)+(R(J+1,K)-R(J,K))/(4^K-1);
   end
   err=abs(R(J,J)-R(J+1,K+1));
end

quad=R(J+1,J+1);

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