simpadpt.m

various matlab programs to slove various problems

function [integ,xfv,nfv]=simpadpt(a,b,tol,fun,hmin);
integ=0; level=0; i=1; alfa(i)=a; beta(i)=b; 
step=(beta(i)-alfa(i))/4; nfv=0;
for k=1:5, x=a+(k-1)*step; f(i,k)=eval(fun); nfv=nfv+1; end
while (i > 0),
 S=0;  S2=0; h=(beta(i)-alfa(i))/2; S=(h/3)*(f(i,1)+4*f(i,3)+f(i,5)); 
 h=h/2; S2=(h/3)*(f(i,1)+4*f(i,2)+f(i,3)); 
 S2=S2+(h/3)*(f(i,3)+4*f(i,4)+f(i,5));
 tolrv=tol*(beta(i)-alfa(i))/(b-a); errrv=abs(S-S2)/10;
 if (errrv > tolrv)
  i=i+1; alfa(i)=alfa(i-1); beta(i)=(alfa(i-1)+beta(i-1))/2;
  f(i,1)=f(i-1,1);f(i,3)=f(i-1,2);f(i,5)=f(i-1,3);len=abs(beta(i)-alfa(i));
  if (len >= hmin),
   if (len <= 11*hmin)
    disp(' Steplength close to hmin  '), 
    str=sprintf('The approximate integral is %12.7e',integ);disp(str),end; 
    step=len/4; x=alfa(i)+step; f(i,2)=eval(fun); 
    nfv=nfv+1; x=beta(i)-step; f(i,4)=eval(fun); nfv=nfv+1;
   else, xfv=xfv'; disp(' Too small steplength   ')
    str=sprintf('The approximate integral is %12.7e',integ);
    disp(str), return 
  end, else    
  integ=integ+S2; level=level+1; if (level==1),
  for k=1:5, xfv(k)=alfa(i)+(k-1)*h; end; ist=5;
 else, for k=1:4, xfv(ist+k)=alfa(i)+k*h; end; ist=ist+4; end;   
  if (beta(i)==b), xfv=xfv'; 
  str=sprintf('The approximate integral is %12.7e',integ); 
  disp(str), return, end; i=i-1; alfa(i)=beta(i+1); 
  f(i,1)=f(i+1,5); f(i,3)=f(i,4); step=abs(beta(i)-alfa(i))/4; 
  x=alfa(i)+step; f(i,2)=eval(fun); nfv=nfv+1; x=beta(i)-step; 
  f(i,4)=eval(fun); nfv=nfv+1;
 end
end