Code covered by the BSD License

# Numerical Methods Using MATLAB, 3e

### John Mathews (view profile)

20 Aug 2002 (Updated )

Companion Software

```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