Home > K25104 > Integration > milnes_rule.m

milnes_rule

PURPOSE ^

Employs Milne's rule to integrate f between a and b

SYNOPSIS ^

function [ Q ] = milnes_rule( f,a,b )

DESCRIPTION ^

 Employs Milne's rule to integrate f between a and b
 Input arguments:
   f, function handle
   a,b, integration bounds, a<b
 Output arguments:
   Q, value of integral

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [ Q ] = milnes_rule( f,a,b )
0002 % Employs Milne's rule to integrate f between a and b
0003 % Input arguments:
0004 %   f, function handle
0005 %   a,b, integration bounds, a<b
0006 % Output arguments:
0007 %   Q, value of integral
0008 
0009 % first check user inputs
0010 if isa(f,'function_handle')==0;
0011     error('input must be a function handle');
0012 elseif a>=b;
0013     error('invalid interval');
0014 end
0015 
0016 f1=feval(f,(3*a+b)/4);      % evaluate f at (3a+b)/4
0017 f2=feval(f,(a+b)/2);        % evaluate f at (a+b)/2
0018 f3=feval(f,(a+3*b)/4);      % evaluate f at (a+3b)/4
0019 
0020 Q=(b-a)*(2*f1-f2+2*f3)/3;   % evalaute Q according to Milne's rule
0021 
0022 end
0023

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