Solving PDEs by means of cellular automata

Some physical phenomena can be simulated by means of CAs. In this page we have prepared a CA to simulate the spread of molecules in space, or the spread of heat in a material.
The sites of a square lattice have values that represents concentration or temperature. At each update, a site's value is replaced by the average of the eight nearest neighbors in its Moore neighborhood.
Indeed, this is not a pure CA, because we let grid nodes to have continuous values.

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 2/1/2000 by Juan de Lara (, need help for using this courses?.

The OOCSMP code - The SODA code