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'), endendA = zeros(n,n); h = 1/n;% 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