📄 simptol.mht

📁 it is a very essential matlab code.

💻 MHT

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<BODY><PRE>function [z, n] =3D simptol(func,a,b,tol)
% Routine for Simpson's 1/3 rule integration to specified tolerance.
%
% USAGE:  [z, n] =3D traptol('function',a,b,tol)
%
% input:  function =3D name of external function file.  This file
%             must be able to receive a vector of x data as input=20
%	      and produce a vector of y data as output
%         a, b     =3D limits of integration
%         tol      =3D absolute error tolerance in answer
% output: z        =3D value of integral of function between a and b
%         n        =3D number of intervals required to obtained desired =
accuracy

% NOTE: in this routine n refers to the number of segments in the
%   interval from a to b

% first integral using 2 segments
n =3D 2;
h =3D (b-a)/n;
x =3D linspace(a,b,n+1);
y =3D feval(func,x);
z1 =3D h*simpson(y);

abserror =3D Inf;
% start looping with doubled N
while abserror &gt; tol
  n =3D 2*n;
  h =3D (b-a)/n;
  x =3D linspace(a,b,n+1);
  y =3D feval(func,x);
  z2 =3D h*simpson(y);
  abserror =3D abs(z2 - z1);
  z1 =3D z2; % store this for next loop
end

z =3D z2;

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