simpadpt.m

sareli<matlab科学计算>配套程序

function [JSf,nodes]=simpadpt(f,a,b,tol,hmin)
%SIMPADPT   Numerically evaluate integral, adaptive Simpson quadrature.
%   JSF = SIMPADPT(FUN,A,B,TOL,HMIN) tries to approximate the integral of function
%   FUN from A to B to within an error of TOL using recursive
%   adaptive Simpson quadrature.  The inline function Y = FUN(V) should
%   accept a vector argument V and return a vector result Y, the
%   integrand evaluated at each element of X.  
%  
%    [JSF,NODES] = SIMPADPT(...) returns the distribution of nodes. 
A=[a,b]; N=[]; S=[]; JSf = 0; ba = b - a; nodes=[];
while ~isempty(A),  
  [deltaI,ISc]=caldeltai(A,f);
  if abs(deltaI) <= 15*tol*(A(2)-A(1))/ba;
     JSf = JSf + ISc;  
     S = union(S,A); 
     nodes = [nodes, A(1) (A(1)+A(2))*0.5 A(2)];
     S = [S(1), S(end)]; A = N; N = [];
  elseif A(2)-A(1) < hmin
     JSf=JSf+ISc; 
     S = union(S,A); 
     S = [S(1), S(end)]; A=N; N=[];
     warning('Too small step-length');
  else
     Am = (A(1)+A(2))*0.5; 
     A = [A(1) Am]; 
     N = [Am, b];
  end
end  
nodes=unique(nodes);
return

function [deltaI,ISc]=caldeltai(A,f)
L=A(2)-A(1); 
t=[0; 0.25; 0.5; 0.5; 0.75; 1];
x=L*t+A(1);  
L=L/6;  
w=[1; 4; 1];   
fx=feval(f,x);
IS=L*sum(fx([1 3 6]).*w);  
ISc=0.5*L*sum(fx.*[w;w]); 
deltaI=IS-ISc;
return