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Numerical Methods Using MATLAB, 3e

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Numerical Methods Using MATLAB, 3e

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20 Aug 2002 (Updated )

Companion Software

[D,err,relerr,n]=diffext(f,x,delta,toler)
function [D,err,relerr,n]=diffext(f,x,delta,toler)

%Input  - f is the function input as a string 'f'
%       - x is the differentiation point
%       - delta is the tolerance for the error
%       - toler is the tolerance for the relative error
%Output - D is the matrix of approximate derivatives
%       - err is the error bound
%       - relerr is the relative error bound
%       - n is the coordiante of the "best approximation"

% 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

err=1;
relerr=1;
h=1;
j=1;
D(1,1)=(feval(f,x+h)-feval(f,x-h))/(2*h);

while relerr > toler & err > delta &j <12
   h=h/2;
   D(j+1,1)=(feval(f,x+h)-feval(f,x-h))/(2*h);
   for k=1:j
      D(j+1,k+1)=D(j+1,k)+(D(j+1,k)-D(j,k))/((4^k)-1);
   end
   err=abs(D(j+1,j+1)-D(j,j));
   relerr=2*err/(abs(D(j+1,j+1))+abs(D(j,j))+eps);
   j=j+1;
end

[n,n]=size(D);

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