1. Parabolic Equation

3. Cari u(x,t) yang memenuhi persamaan Parabolik Dengan syarat batas u(x,0) = 0 = u(8,t) dan u(x,0) = 4x – ½ x 2 di x = i : i = 0, 1, 2, 3,… 5.

4. Solution : c 2 = 4, h = 1, k = 1/8

11. Lab 1 Discussion In lab 1 we solved the advection equation: The first method we tried was the forward Euler method:

12. Upwind method, CFL=0.9

13. What’s Going On? AdvectionDiffusion Add/subtract

14. Numerical Diffusion The alebgra shows that the finite difference equation has both an advective term and a diffusive term. It is in fact a better model for:

15. Upwind method, CFL=1.2 (final timstep only) Instability

16. Lax-Wendroff method, CFL=0.9

17. Flux Limiters In the advection equation let’s assume v is positive: Most flux limiters are based on the ratio of the first order fluxes at node i, i.e.: