clear
disp('Application to time dependent heat diffusion')
A = (.016)*[-2 1 0;1 -2 1;0 1 -2]
pause
f = [ 1 1 1]'
pause
xp_sol = -A\f
pause
[u d] = eig(A)
pause
x0 = [0 0 0]'
pause
c = u\(x0 -  xp_sol)
pause
syms t
disp('x = c(1)*u(:,1)*exp(d(1,1)*t) + c(2)*u(:,2)*exp(d(2,2)*t) +c(3)*u(:,3)*exp(d(3,3)*t) + xp_sol')
pause
x = c(1)*u(:,1)*exp(d(1,1)*t) + c(2)*u(:,2)*exp(d(2,2)*t) +c(3)*u(:,3)*exp(d(3,3)*t) + xp_sol
pause
ezplot(x(1),[0 500])
hold on
ezplot(x(2),[0 500])
ezplot(x(3),[0 500])