The Heat equation in 1-D

The next is an applet that solves the Heat (time dependent) equation in 1-D : (d/dt)u-K*(d2/dxx)u = 0. The equation is solved using the finite difference method.

We want to solve the equation for two connected bars, each of length 5, and with different value for parameter K. We can model a class nambed Bar, and encapsulate the equation in it, then we will connect them, setting the left boundary conditions of the second bar as the temperature of the first bar at the right end, and the right boundary conditions for the first bar as the temperature at the left of the second bar. During simulation , we put a temperature of 10 degrees at the left end of the first bar, and at the right end of the second bar. Initially, the bars have a temperature of 0 degrees. The evolution of the first bar's temperature can be seen in the following simulation :

Theory pages:
Main page
FEM (i)
FEM (ii)
FDM (i)
Example pages:
1-d Heat Equation
2-d steady state Heat Equation
2-d Heat Equation
1-d non diffusive transport equation
1-d diffusive transport equation
2-d Non diffusive transport equation
Mesh generation with OOCSMP
Moving grids
Application pages:
Heating of two beams
Heating of two moving beams
Solving the equation Ut+Uxx+Uxy+Uyx=0
Solving the equation Ut+Uxx+Uxy+Uyx=0 using MGEN
Heat 1d using several outputs
Solving the Heat equation with a CA
Comparing a CA with the FEM
Gordon's sine equation

Other courses
Other pages

Last modified 22/12/99 by Juan de Lara (, need help for using this courses?.

The OOCSMP code - The SODA code