Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific...
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![Page 1: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/1.jpg)
Scientific Computing LabResults Worksheet 4
Dr. Miriam Mehl
Institut fürInformatik
Scientific Computingin
Computer Science
![Page 2: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/2.jpg)
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 end
![Page 3: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/3.jpg)
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))+…
endend 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 end res=sqrt(res/(N_x*N_y));
end
![Page 4: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/4.jpg)
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);endt=t+dt;
![Page 5: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/5.jpg)
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=0
![Page 6: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/6.jpg)
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=1/8
![Page 7: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/7.jpg)
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=2/8
![Page 8: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/8.jpg)
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=3/8
![Page 9: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/9.jpg)
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=4/8
![Page 10: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/10.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=0
![Page 11: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/11.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=1/8
![Page 12: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/12.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=2/8
![Page 13: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/13.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=3/8
![Page 14: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/14.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=4/8
![Page 15: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/15.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=0
![Page 16: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/16.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=1/8
![Page 17: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/17.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=2/8
![Page 18: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/18.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=3/8
![Page 19: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/19.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=4/8
![Page 20: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/20.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=0
![Page 21: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/21.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=1/8
![Page 22: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/22.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=2/8
![Page 23: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/23.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=3/8
![Page 24: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/24.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=4/8
![Page 25: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/25.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=0
![Page 26: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/26.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=1/8
![Page 27: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/27.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=2/8
![Page 28: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/28.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=3/8
![Page 29: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/29.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=4/8
![Page 30: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/30.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=0
![Page 31: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/31.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=1/8
![Page 32: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/32.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=2/8
![Page 33: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/33.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=3/8
![Page 34: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/34.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=3/8
![Page 35: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/35.jpg)
Worksheet 4 – stable cases
![Page 36: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/36.jpg)
Worksheet 4 – unstable cases
![Page 37: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/37.jpg)
Worksheet 4 – Solution
x------1/32xxx----1/16xxxxx--1/8xxxxxxx1/4
1/40961/20481/10241/5121/2561/1281/64h/dt
dt<h2/2
![Page 38: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/38.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=0
![Page 39: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/39.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=1/8
![Page 40: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/40.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=2/8
![Page 41: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/41.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=3/8
![Page 42: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/42.jpg)
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=4/8
![Page 43: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/43.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=0
![Page 44: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/44.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=1/8
![Page 45: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/45.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=2/8
![Page 46: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/46.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=3/8
![Page 47: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/47.jpg)
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=4/8
![Page 48: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/48.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=0
![Page 49: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/49.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=1/8
![Page 50: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/50.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=2/8
![Page 51: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/51.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=3/8
![Page 52: Scientific Computing Lab Results Worksheet 4 Dr. Miriam Mehl Institut fr Informatik Scientific Computing in Computer Science.](https://reader035.fdocuments.us/reader035/viewer/2022062413/5a4d1b8e7f8b9ab0599c04e8/html5/thumbnails/52.jpg)
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=4/8