Discrete 
Continuous 

Model: 
Values change instantly, at clock ticks. 
Values change smoothly. 
Material: 
Atoms 
Metal 
Light: 
Photons 
Electromagnetic waves 
Written: 
Computer program 
System of equations 
Unit: 
Expression 
Partial differential equation (PDE) 
Domain: 
Computer Science 
Applied Mathematics 
Benefits: 
Easy to compute. Solutions are
wellposed. 
Easy to vary in space and time.
Equations always stable. 
Drawbacks: 
Roundoff. Stability.
Conservation. The code! 
Illposed problems (singularities). The
math! 
Discrete 
Finite 
Continous 
B = (right.z  left.z) / grid_size_x; 
B=∆z/∆x  B = dz/dx (or ∂z/∂x) 
C = (new.z  old.z) / dt; 
C=∆z/∆t  C = dz/dt 
new.z = old.z + C*dt; 
∆z=C*∆t  C = dz/dt 
P += V*dt;  ∆P=V*∆t  dP/dt = V 
Here: