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