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

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

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

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;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Worksheet 4 – stable cases

Worksheet 4 – unstable cases

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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