function [t,err]=expliciterr(dx);
% EXPLICITERR  For reproducing figure 2.4 in Morton & Mayers.
% At command line:
%  >> [t1,err1]=expliciterr(0.1); [t2,err2]=expliciterr(0.05);
%  >> semilogy(t1,err1,t2,err2)
%  >> xlabel('t_n'), ylabel('E^n'), set(gca,'XTick',0:0.25:1)
% ELB 2/17/05

nu=0.5;  dt=nu*dx^2;  t=0:dt:1;
x=0:dx:1;  J=length(x)-1;  % J is number of space steps
U=x.*(1-x);  % initial condition
% to see i.c. and exact soln:  plot(x,U,x,uexact(x,0.1))

err(1)=0;
for n=1:length(t)-1
    % take explicit step and compare to exact
    U(2:J)=U(2:J) + nu*( U(3:J+1) - 2*U(2:J) + U(1:J-1) );
    err(n+1)=max(abs(uexact(x,n*dt)-U));
end

function y=uexact(x,t);
% Fourier series sum w/o loop!; x is row vector; t must be scalar
N=181;  mm=(1:2:2*N-1)';  pimm=pi*mm;
c=exp(-t*pimm.^2)./(mm.^3);
cc=repmat(c,1,length(x));
y=(8/pi^3)*sum(cc.*sin(pimm*x));