function ch2ex8
% Galerkin scheme as in Fletcher, p. 112.
global J h
N = 20;
h = 1/(N+1);
x = h*(1:N);
v0 = x + sin(pi*x);
e = ones(N,1);
M = spdiags([e  4*e e],-1:1,N,N)/6;
J = spdiags([e -2*e e],-1:1,N,N)/h^2;
options = odeset('Mass',M,'Jacobian',J);
[t,v] = ode15s(@f,[0 0.5],v0,options);
% Add the boundary values:
x = [0 x 1];
npts = length(t);
v = [zeros(npts,1) v ones(npts,1)];
colormap(gray)
surf(x,t,v)
% generate ch2fig7.eps from o view of this.
%=========================================
function dvdt = f(t,v)
global J h
dvdt = J*v;
dvdt(end) = dvdt(end) + 1/h^2;