scientific computing lab results worksheet 4 dr. miriam mehl institut fr informatik scientific...
DESCRIPTION
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)); endTRANSCRIPT
Scientific Computing LabResults Worksheet 4
Dr. Miriam Mehl
Institut fürInformatik
Scientific Computingin
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 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))+…
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
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;
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=0
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=1/8
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=2/8
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=3/8
Worksheet 4 – Solution
Nx= Ny=3,
dt=1/64
t=4/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=0
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=1/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=2/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=3/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
t=4/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=0
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=1/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=2/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=3/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/256
t=4/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=0
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=1/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=2/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=3/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/256
t=4/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=0
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=1/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=2/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=3/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/1024
t=4/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=0
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=1/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=2/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=3/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/4096
t=3/8
Worksheet 4 – stable cases
Worksheet 4 – unstable cases
Worksheet 4 – Solution
x------1/32xxx----1/16xxxxx--1/8xxxxxxx1/4
1/40961/20481/10241/5121/2561/1281/64h/dt
dt<h2/2
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=0
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=1/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=2/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=3/8
Worksheet 4 – Solution
Nx= Ny=7,
dt=1/64
implicit
t=4/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=0
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=1/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=2/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=3/8
Worksheet 4 – Solution
Nx= Ny=15,
dt=1/64
implicit
t=4/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=0
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=1/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=2/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=3/8
Worksheet 4 – Solution
Nx= Ny=31,
dt=1/64
implicit
t=4/8