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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

[SRmat,quad,err]=adapt(f,a,b,tol)
function [SRmat,quad,err]=adapt(f,a,b,tol)

%Input  - f is the integrand input as a string 'f'
%       - a and b are upper and lower limits of integration
%       - tol is the tolerance
%Output - SRmat is the table of values
%       - quad is the quadrature value
%       - err is the error estimate

% 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

%Initialize values

SRmat = zeros(30,6);
iterating=0;
done=1;
SRvec=zeros(1,6);
SRvec=srule(f,a,b,tol);
SRmat(1,1:6)=SRvec;
m=1;
state=iterating;

while(state==iterating)
   n=m;
   for j=n:-1:1
      p=j;
      SR0vec=SRmat(p,:);
      err=SR0vec(5);
      tol=SR0vec(6);
      if (tol<=err)
         
         %Bisect interval,apply Simpson's rule
         %recursively, and determine error
         state=done;
         SR1vec=SR0vec;
         SR2vec=SR0vec;
         a=SR0vec(1);
         b=SR0vec(2);
         c=(a+b)/2;
         err=SR0vec(5);
         tol=SR0vec(6);
         tol2=tol/2;
         SR1vec=srule(f,a,c,tol2);
         SR2vec=srule(f,c,b,tol2);
         err=abs(SR0vec(3)-SR1vec(3)-SR2vec(3))/10;
         
         %Accuracy test
         if (err<tol)
            SRmat(p,:)=SR0vec;
            SRmat(p,4)=SR1vec(3)+SR2vec(3);
            SRmat(p,5)=err;
         else
            SRmat(p+1:m+1,:)=SRmat(p:m,:);
            m=m+1;
            SRmat(p,:)=SR1vec;
            SRmat(p+1,:)=SR2vec;
            state=iterating;
         end
      end
   end
end

quad=sum(SRmat(:,4));
err=sum(abs(SRmat(:,5)));
SRmat=SRmat(1:m,1:6);

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