forked from burakbayramli/books
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathconvergence_test_periodic.m
117 lines (108 loc) · 2.91 KB
/
convergence_test_periodic.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
t_0 = 0; t_f = 1; N = 10; M = 10;
for j=1:9
[u,u_exact,x,t] = explicit_upwind_periodic(@g,t_0,t_f,M,N);
err_inf(j) = max(abs(u(:,M+1)-u_exact(:,M+1)));
err_one(j) = sum((x(2)-x(1))*abs(u(:,M+1)-u_exact(:,M+1)));
err_two(j) = sqrt(sum((x(2)-x(1))*(u(:,M+1)-u_exact(:,M+1)).^2));
Dt(j) = (t_f-t_0)/M;
Dx(j) = 2*pi/N;
N = 2*N; M = 2*M;
end
err_inf
err_two
err_one
display('Explicit Upwind ratios')
err_inf(1:8)./err_inf(2:9)
err_two(1:8)./err_two(2:9)
err_one(1:8)./err_one(2:9)
figure(1)
clf
plot(log10(Dx),log10(err_inf));
hold on
plot(log10(Dt),log10(err_inf));
plot(log10(Dx),log10(err_one),'r');
plot(log10(Dt),log10(err_one),'r');
plot(log10(Dx),log10(err_two),'b');
plot(log10(Dt),log10(err_two),'b');
hold off
t_0 = 0; t_f = 1; N = 10; M = 10;
for j=1:9
[u,u_exact,x,t] = lax_friedrichs_periodic(@g,t_0,t_f,M,N);
err_inf(j) = max(abs(u(:,M+1)-u_exact(:,M+1)));
err_one(j) = sum((x(2)-x(1))*abs(u(:,M+1)-u_exact(:,M+1)));
err_two(j) = sqrt(sum((x(2)-x(1))*(u(:,M+1)-u_exact(:,M+1)).^2));
Dt(j) = (t_f-t_0)/M;
Dx(j) = 2*pi/N;
N = 2*N; M = 2*M;
end
err_inf
err_two
err_one
display('Lax Friedrichs ratios')
err_inf(1:8)./err_inf(2:9)
err_two(1:8)./err_two(2:9)
err_one(1:8)./err_one(2:9)
figure(2)
clf
plot(log10(Dx),log10(err_inf));
hold on
plot(log10(Dt),log10(err_inf));
plot(log10(Dx),log10(err_one),'r');
plot(log10(Dt),log10(err_one),'r');
plot(log10(Dx),log10(err_two),'b');
plot(log10(Dt),log10(err_two),'b');
hold off
t_0 = 0; t_f = 1; N = 10; M = 10;
for j=1:9
[u,u_exact,x,t] = lax_wendroff_periodic(@g,t_0,t_f,M,N);
err_inf(j) = max(abs(u(:,M+1)-u_exact(:,M+1)));
err_one(j) = sum((x(2)-x(1))*abs(u(:,M+1)-u_exact(:,M+1)));
err_two(j) = sqrt(sum((x(2)-x(1))*(u(:,M+1)-u_exact(:,M+1)).^2));
Dt(j) = (t_f-t_0)/M;
Dx(j) = 2*pi/N;
N = 2*N; M = 2*M;
end
err_inf
err_two
err_one
display('Lax Wendroff ratios')
err_inf(1:8)./err_inf(2:9)
err_two(1:8)./err_two(2:9)
err_one(1:8)./err_one(2:9)
figure(3)
clf
plot(log10(Dx),log10(err_inf));
hold on
plot(log10(Dt),log10(err_inf));
plot(log10(Dx),log10(err_one),'r');
plot(log10(Dt),log10(err_one),'r');
plot(log10(Dx),log10(err_two),'b');
plot(log10(Dt),log10(err_two),'b');
hold off
t_0 = 0; t_f = 1; N = 10; M = 10;
for j=1:9
[u,u_exact,x,t] = beam_warming_periodic(@g,t_0,t_f,M,N);
err_inf(j) = max(abs(u(:,M+1)-u_exact(:,M+1)));
err_one(j) = sum((x(2)-x(1))*abs(u(:,M+1)-u_exact(:,M+1)));
err_two(j) = sqrt(sum((x(2)-x(1))*(u(:,M+1)-u_exact(:,M+1)).^2));
Dt(j) = (t_f-t_0)/M;
Dx(j) = 2*pi/N;
N = 2*N; M = 2*M;
end
err_inf
err_two
err_one
display('Beam Warming ratios')
err_inf(1:8)./err_inf(2:9)
err_two(1:8)./err_two(2:9)
err_one(1:8)./err_one(2:9)
figure(4)
clf
plot(log10(Dx),log10(err_inf));
hold on
plot(log10(Dt),log10(err_inf));
plot(log10(Dx),log10(err_one),'r');
plot(log10(Dt),log10(err_one),'r');
plot(log10(Dx),log10(err_two),'b');
plot(log10(Dt),log10(err_two),'b');
hold off