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Scientific Computing LabResults Worksheet 2
Dr. Miriam Mehl
Institut fürInformatik
Scientific Computingin
Computer Science
Worksheet 2 – Solution
Worksheet 2 – Solution
1) m-file Euler_implicit.m
for (k=2:size(tk,2)) y_it = y(k-1); dy=1.0; %Newton iteration while (abs(dy)>=0.0001)
dy = (y(k-1) - y_it + dt*rhs(y_it))/ (dt*rhs_y(y_it)-1);
y_it = y_it - dy; end y(k)=y_it;
end
Worksheet 2 – Solution
2) m-file Adams_Moulton.m
y_it = y(k-1); x = y_it + (1/2)*dt*rhs(y_it); %Newton iteration d=1-7*dt+(49/4)*dt^2+(7/5)*dt*x; if (d>0)
dy=1; it=1; while (abs(dy)>0.0001) …
Worksheet 2 – Solution
3) m-file AdamsMoulton_linear_1.m
for (k=2:size(tk,2)) a=(1/2)*dt*7*y(k-1); y(k)=(y(k-1)+2*a-(a/10)*y(k-1))/
(1+(a/10)); end
Worksheet 2 – Solution
Worksheet 2 – Solution
Worksheet 2 – Solution
Worksheet 2 – Solution
Worksheet 2 – Solution
Worksheet 2 – Solution
Worksheet 2 – Solution
Worksheet 2 – Solution
dt 1/2 1/4 1/8 1/16 1/32
error – – 2.0595 0.4854 0.1754
error red. – – – 4.24 2.77
explicit Euler
q=1
Worksheet 2 – Solution
dt 1/2 1/4 1/8 1/16 1/32
error – – 0.0950 0.0938 0.0235
error red. – – – 1.01 3.99
Heun
q=2
Worksheet 2 – Solution
dt 1/2 1/4 1/8 1/16 1/32
error 0.5781 0.5151 0.3665 0.2233 0.1245
error red. – 1.12 1.41 1.64 1.79
implicit Euler
q=1
Worksheet 2 – Solution
dt 1/2 1/4 1/8 1/16 1/32
error – 1.4730 0.3035 0.0704 0.0167
error red. – – 4.85 4.31 4.21
Adams Moulton
q=2
Worksheet 2 – Solution
dt 1/2 1/4 1/8 1/16 1/32
error 1.8196 0.8402 0.3342 0.1237 0.0488
error red. – 2.17 2.51 2.69 2.53
Adams Moulton linearisation 1
q=1
Worksheet 2 – Solution
dt 1/2 1/4 1/8 1/16 1/32
error 18.856 2.1543 0.7990 0.2326 0.1220
error red. – 8.75 2.70 2.73 2.40
Adams Moulton linearisation 2
q=1
Worksheet 2 – Solution
dt Expl. Euler
Heun Impl. Euler
Adams Moulton
Adams Moulton
l1
Adams Moulton
l2
1/2 X – X O
1/4 X X X X
1/8 X X X X X X
1/16 X X X X X X
1/32 X X X X X X