# Heat equation

- Author:
- Juan Carlos Ponce Campuzano

Consider a thin rod of length

*L*with an initial temperature*f*(*x*) throughout and whose ends are held at temperature zero for all time*t*>0. The temperature u(*x,t*) in the rod is determined from the boundary-value problem: u_{t}(*x,t*)=au_{xx}(*x,t*), 0<*x*<*L*,*t*>0; u(0,*t*)=0, u(*L*,t)=0,*t*>0; u(*x*,0)=f(*x*), 0<*x*<*L*. In the following simulation, the temperature u(x,t) is graphed as a function of*x*for various times.**Things to try:**- Change the initial condition u(x,0)=f(x).
- Increase
**n**, the number of terms in the solution. - Change the length
**L**.