1. Finite difference time domain
FDTD -- MATLAB

2. Development of the technique
“advection” equation

3. Calculate the spatial distribution at the next increment in time
Setup a mesh in time and in space. The mesh in position extends beyond the points of interest.
Initial conditions
@ t = 0
time
Calculate the spatial distribution at the next increment in time
@ t = 1
position

4. Invoke periodic boundary conditions

5. Foreword difference in time
Central difference in space

6. Finite difference
Time domain “fdtd”

7. This is valid only for the interior range
2  n  N – 1

8. Periodic boundary conditions

9. Time  #1
-3L/8
-1/2 #2
-1L/8 1 #3
+1L/8
3/2 #4
+3L/8

10. Example of the FDTD using the above procedure
Initial conditions
Time  2 3 4
-3L/8
-1/2
5/2 z
-1L/8 1
-3/2
+1L/8
3/2
+3L/8

11. Lax to the rescue!

12. Periodic boundary conditions

13.  #1
-3L/8 #2
-1L/8 1 #3
+1L/8 #4
+3L/8

14. Example of the FDTD using the Lax procedure.
Initial conditions
Time  2 3 4
-3L/8 1 z
-1L/8
+1L/8
+3L/8

15. First iteration & 50th iteration

16. Movie to illustrate the calculation

17. Frasson

18. Lewandowski