e861.m

matlab算法集 matlab算法集

%------------------------------------------------------------------
% Example 8.6.1: Extrapolation Method                             
%------------------------------------------------------------------
   clc
   clear
   q = 5000;
   n = 3;
   m = 9;
   alpha = 0;	
   beta	= 4.0;
   h = (beta-alpha)/(m-1);
   tol = 1.e-7;
   x0 = [1 -3 6]';
   p = zeros (m-1,1);
   t = zeros (m,1);
   e = zeros (m-1,1);
   X = zeros (m,n);
   E = zeros (m-1,n);

% Exact solution 

   fprintf ('Example 8.6.1: Extrapolation Method\n');
   for k = 1 : m
      t(k) = (k - 1)*h;
      X(k,1) = -t(k)*exp(-t(k)) +   exp(-2*t(k));
      X(k,2) = (t(k)-1)*exp(-t(k)) - 2*exp(-2*t(k));
      X(k,3) = (2-t(k))*exp(-t(k)) + 4*exp(-2*t(k));
   end
   graphxy (t,X,'Exact Solution','t','x')  
 
% Extrapolation method 

   for k = 1 : m-1
      [x0,e(k),p(k)] = bsext0 (x0,t(k),t(k+1),tol,q,'funf861');
      for j = 1 : n
         E(k,j) = x0(j) - X(k+1,j);
      end
   end

% Display results 
         
   fprintf ('\n t   evaluations   ||E||(local)    ||E||(global)\n'); 
   fprintf ('------------------------------------------------\n');
   for k = 1 : m-1
      fprintf ('%3.1f %8i      %12.7e  %12.7e\n',...
               t(k+1),p(k),e(k),norm(E(k,:),inf));
   end
   fprintf ('------------------------------------------------\n');
   wait
%------------------------------------------------------------------