1. Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut für Informatik Scientific Computing in Computer Science

2. Worksheet 4 – Solution 1) m-file Euler.m x_old=x_m; %time step for k=2:N_x+1 for m=2:N_y+1 x_m(k,m) = x_old(k,m) + dt*(d_1*(x_old(k-1,m)+x_old(k+1,m))+… end

3. Worksheet 4 – Solution 2) m-file Euler_implicit.m while (res>0.0001) res=0.0; for m=2:N_y+1 for k=2:N_x+1 x_m(k,m)=(d_1*(x_m(k-1,m)+x_m(k+1,m))+… end for m=2:N_y+1 for k=2:N_x+1 res=res+(b((m-2)*N_x+k-1)+a_ii*x_m(k,m)-… end res=sqrt(res/(N_x*N_y)); end

4. Worksheet 4 – Solution 3) m-file worksheet4.m while (t<T_end) if (n==1) x_m=Euler(N_x,N_y,dt,x_m); else x_m=Euler_implicit(N_x,N_y,dt,x_m); end t=t+dt;

5. Worksheet 4 – Solution N x = N y =3, dt=1/64 t=0

6. Worksheet 4 – Solution N x = N y =3, dt=1/64 t=1/8

7. Worksheet 4 – Solution N x = N y =3, dt=1/64 t=2/8

8. Worksheet 4 – Solution N x = N y =3, dt=1/64 t=3/8

9. Worksheet 4 – Solution N x = N y =3, dt=1/64 t=4/8

10. Worksheet 4 – Solution N x = N y =7, dt=1/64 t=0

11. Worksheet 4 – Solution N x = N y =7, dt=1/64 t=1/8

12. Worksheet 4 – Solution N x = N y =7, dt=1/64 t=2/8

13. Worksheet 4 – Solution N x = N y =7, dt=1/64 t=3/8

14. Worksheet 4 – Solution N x = N y =7, dt=1/64 t=4/8

15. Worksheet 4 – Solution N x = N y =7, dt=1/256 t=0

16. Worksheet 4 – Solution N x = N y =7, dt=1/256 t=1/8

17. Worksheet 4 – Solution N x = N y =7, dt=1/256 t=2/8

18. Worksheet 4 – Solution N x = N y =7, dt=1/256 t=3/8

19. Worksheet 4 – Solution N x = N y =7, dt=1/256 t=4/8

20. Worksheet 4 – Solution N x = N y =15, dt=1/256 t=0

21. Worksheet 4 – Solution N x = N y =15, dt=1/256 t=1/8

22. Worksheet 4 – Solution N x = N y =15, dt=1/256 t=2/8

23. Worksheet 4 – Solution N x = N y =15, dt=1/256 t=3/8

24. Worksheet 4 – Solution N x = N y =15, dt=1/256 t=4/8

25. Worksheet 4 – Solution N x = N y =15, dt=1/1024 t=0

26. Worksheet 4 – Solution N x = N y =15, dt=1/1024 t=1/8

27. Worksheet 4 – Solution N x = N y =15, dt=1/1024 t=2/8

28. Worksheet 4 – Solution N x = N y =15, dt=1/1024 t=3/8

29. Worksheet 4 – Solution N x = N y =15, dt=1/1024 t=4/8

30. Worksheet 4 – Solution N x = N y =31, dt=1/4096 t=0

31. Worksheet 4 – Solution N x = N y =31, dt=1/4096 t=1/8

32. Worksheet 4 – Solution N x = N y =31, dt=1/4096 t=2/8

33. Worksheet 4 – Solution N x = N y =31, dt=1/4096 t=3/8

34. Worksheet 4 – Solution N x = N y =31, dt=1/4096 t=3/8

35. Worksheet 4 – stable cases

36. Worksheet 4 – unstable cases

37. Worksheet 4 – Solution x------1/32 xxx----1/16 xxxxx--1/8 xxxxxxx1/4 1/40961/20481/10241/5121/2561/1281/64h/dt dt<h 2 /2

38. Worksheet 4 – Solution N x = N y =7, dt=1/64 implicit t=0

39. Worksheet 4 – Solution N x = N y =7, dt=1/64 implicit t=1/8

40. Worksheet 4 – Solution N x = N y =7, dt=1/64 implicit t=2/8

41. Worksheet 4 – Solution N x = N y =7, dt=1/64 implicit t=3/8

42. Worksheet 4 – Solution N x = N y =7, dt=1/64 implicit t=4/8

43. Worksheet 4 – Solution N x = N y =15, dt=1/64 implicit t=0

44. Worksheet 4 – Solution N x = N y =15, dt=1/64 implicit t=1/8

45. Worksheet 4 – Solution N x = N y =15, dt=1/64 implicit t=2/8

46. Worksheet 4 – Solution N x = N y =15, dt=1/64 implicit t=3/8

47. Worksheet 4 – Solution N x = N y =15, dt=1/64 implicit t=4/8

48. Worksheet 4 – Solution N x = N y =31, dt=1/64 implicit t=0

49. Worksheet 4 – Solution N x = N y =31, dt=1/64 implicit t=1/8

50. Worksheet 4 – Solution N x = N y =31, dt=1/64 implicit t=2/8

51. Worksheet 4 – Solution N x = N y =31, dt=1/64 implicit t=3/8

52. Worksheet 4 – Solution N x = N y =31, dt=1/64 implicit t=4/8