Kurt Frischmuth: Partial Differential Equations

Kurt Frischmuth

Lecture

Partial Differential Equations - Numerical Methods

for Computational Engineers




Some Examples

(some) wave - exact solution (on some grid)

a simple wave.


some (other) wave - numerical solution by Lax-Friedrich Method (on different grid)

Lax-Friedrich Method



yet another wave - numerical solution by Lax-Wendroff Method

Lax-Wendroff Method



nonlinear wave - Burgers equation, numerical solution by Lax-Friedrich Method

Lax-Friedrich Method on Burgers equation
heat conduction - explicit scheme (at the onset of instability)

heat conduction.


heat conduction - implicit scheme (stable, despite smaller x-step)

heat conduction.


heat conduction - iterative solution (stationary case)

heat conduction.