function [tp,yp,abserr] = colloc2(n);
%
%   function [t,y,abserr] = colloc2(n);
%
% Solves the linear BVP from page 3.61
% using collocation with sines.
%

Np = 1000;
h  = 1.0 / (n+1);
t  = linspace(h,1.0-h,n);
tp = linspace(0.0,1.0,Np);

% Determine the right-hand side vector

g = (400 * (cos(pi*t)).^2 + 2*pi^2 * cos(2*pi*t))';

% Determine the matrices from the evaluation of y'' and y

A1 = zeros(n,n);
A2 = A1;

for l=1:n
    for k=1:n
        A1(l,k) = -k*k*pi*pi*sin(k*pi*t(l));
        A2(l,k) = sin(k*pi*t(l));
    end;
end;

% Solve the linear system

A = A1 - 400.0 * A2;

x = (A \ g)';

% Compute the exact solution and the absolute error

yexact = -(cos(pi*tp)).^2 + (exp(20*(tp-1)) + exp(-20*tp))/(1+exp(-20));
yp     = 0.0 * tp;

for k=1:n
    yp = yp + x(k)*sin(k*pi*tp);
end;

abserr = norm(yp-yexact,inf);