function [A,b,x] = wing(n,t1,t2) 
%WING Test problem with a discontinuous solution. 
% 
% [A,b,x] = wing(n,t1,t2) 
% 
% Discretization of a first kind Fredholm integral eqaution with 
% kernel K and right-hand side g given by 
%    K(s,t) = t*exp(-s*t^2)                       0 < s,t < 1 
%    g(s)   = (exp(-s*t1^2) - exp(-s*t2^2)/(2*s)  0 < s   < 1 
% and with the solution f given by 
%    f(t) = | 1  for  t1 < t < t2 
%           | 0  elsewhere. 
% 
% Here, t1 and t2 are constants satisfying t1 < t2.  If they are 
% not speficied, the values t1 = 1/3 and t2 = 2/3 are used. 
 
% Reference: G. M. Wing, "A Primer on Integral Equations of the 
% First Kind", SIAM, 1991; p. 109. 
 
% Discretized by Galerkin method with orthonormal box functions; 
% both integrations are done by the midpoint rule. 
 
% Per Christian Hansen, IMM, 09/17/92. 
 
% Initialization. 
if (nargin==1) 
  t1 = 1/3; t2 = 2/3; 
else 
  if (t1 > t2), error('t1 must be smaller than t2'), end 
end 
A = zeros(n,n); h = 1/n; sh = sqrt(h); 
 
% Set up matrix. 
sti = ([1:n]-0.5)*h; 
for i=1:n 
  A(i,:) = h*sti.*exp(-sti(i)*sti.^2); 
end 
 
% Set up right-hand side. 
if (nargout > 1) 
  b = sqrt(h)*0.5*(exp(-sti*t1^2)' - exp(-sti*t2^2)')./sti'; 
end 
 
% Set up solution. 
if (nargout==3) 
  I = find(t1 < sti & sti < t2); 
  x = zeros(n,1); x(I) = sqrt(h)*ones(length(I),1); 
end 
