# 3.6, Example 1, Bar with insulated ends
# Heat equation on a bar , f(x)=100, zero at ends
F:=(m,x)->(400/Pi)*(1/(2*m+1))*sin(2*m*x+x);
S:=(N,x)->sum(F(m,x),m=0..N):
opts:=axes=boxed,thickness=2:
n:=2:plot(S(n,x),x=-Pi..Pi,opts);S(n,x);
# Snapshot plots
u:=(x,t,N)->sum(F(m,x)*exp(-(2*m+1)^2*t),m=0..N):
plot(u(x,0,6),x=0..Pi,opts);
plot(u(x,1.5,6),x=0..Pi,opts);
plot(u(x,2.5,6),x=0..Pi,opts);
with(plots):
animate( plot, [u(x,t,6),x=0..Pi,opts], t=0..3, trace=5, frames=20 );