romber.m

关于数值计算的matlab程序代码,包含了很多的实用的算法.程序全部可以直接用的,有详细的英文注释.

function [R,quad,err,h]=romber(f,a,b,n,tol)

%Input  - f is the integrand input as a string 'f'
%       - a and b are upper and lower limits of integration
%       - n is the maximum number of rows in the table
%       - tol is the tolerance
%Output - R is the Romberg table
%       - quad is the quadrature value
%       - err is the error estimate
%       - h is the smallest step size used

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

M=1;
h=b-a;
err=1;
J=0;
R=zeros(4,4);
R(1,1)=h*(feval(f,a)+feval(f,b))/2;

while((err>tol)&(J<n))|(J<4)
   J=J+1;
   h=h/2;
   s=0;
   for p=1:M
      x=a+h*(2*p-1);
      s=s+feval(f,x);
   end
   R(J+1,1)=R(J,1)/2+h*s;
   M=2*M;
   for K=1:J
      R(J+1,K+1)=R(J+1,K)+(R(J+1,K)-R(J,K))/(4^K-1);
   end
   err=abs(R(J,J)-R(J+1,K+1));
end

quad=R(J+1,J+1);