CN-Lista03.gab

Prévia do material em texto

3ª Lista de Exercícios - Gabarito
Cálculo Numérico Profª Natalia Silveira
1ª Questão
x f(x) g(x)
1.0 1.0 1.0
1.1 1.2 1.1
1.2 1.5 1.2
1.3 1.9 1.5
1.4 2.3 2.0
1.5 2.9 2.5
1.6 3.5 3.2
1.7 4.2 3.9
1.8 5.0 4.8
1.9 6.0 5.9
2.0 7.0 7.0
2.1 8.2 8.3
2.2 9.4 9.6
2.3 10.9 11.1
2.4 12.4 12.8
2.5 14.1 14.5
2.6 16.0 16.4
2.7 18.0 18.3
2.8 20.2 20.4
2.9 22.5 22.7
3.0 25.0 25.0
0.0
5.0
10.0
15.0
20.0
25.0
1.0 1.5 2.0 2.5 3.0
f(x)
g(x)
2ª Questão
x f(x) g(x)
0.000000 1.0 1.0
0.078540 0.8 1.0
0.157080 0.7 0.9
0.235619 0.5 0.8
0.314159 0.3 0.7
0.392699 0.2 0.5
0.471239 0.0 0.3
0.549779 -0.2 0.1
0.628319 -0.4 -0.2
0.706858 -0.5 -0.4
0.785398 -0.7 -0.7
0.863938 -0.9 -1.0
0.942478 -1.0 -1.2
1.021018 -1.2 -1.4
1.099557 -1.3 -1.6
1.178097 -1.5 -1.8
1.256637 -1.6 -1.9
1.335177 -1.7 -2.0
1.413717 -1.8 -2.1
1.492257 -1.9 -2.1
1.570796 -2.0 -2.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
0.0 0.4 0.8 1.2 1.6
f(x) g(x)
3ª Questão
x f(x) g(x)
0.000000 1.000000 1.000000
0.100000 1.010000 1.083155
0.200000 1.040000 1.170875
0.300000 1.090000 1.262958
0.400000 1.160000 1.359114
0.500000 1.250000 1.458972
0.600000 1.360000 1.562099
0.700000 1.490000 1.668044
0.800000 1.640000 1.776414
0.900000 1.810000 1.887004
1.000000 2.000000 2.000000
1.100000 2.210000 2.116289
1.200000 2.440000 2.237931
1.300000 2.690000 2.368845
1.400000 2.960000 2.515812
1.500000 3.250000 2.689916
1.600000 3.560000 2.908599
1.700000 3.890000 3.198563
1.800000 4.240000 3.599862
1.900000 4.610000 4.171619
2.000000 5.000000 5.000000
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.0 0.5 1.0 1.5 2.0
f(x)
g(x)
4ª Questão
x f(x) g(x)
0.523599 0.577350 0.577350
0.549779 0.612801 0.611426
0.575959 0.649408 0.646822
0.602139 0.687281 0.683714
0.628319 0.726543 0.722282
0.654498 0.767327 0.762719
0.680678 0.809784 0.805221
0.706858 0.854081 0.849992
0.733038 0.900404 0.897238
0.759218 0.948965 0.947170
0.785398 1.000000 1.000000
0.811578 1.053780 1.055940
0.837758 1.110613 1.115200
0.863938 1.170850 1.177986
0.890118 1.234897 1.244501
0.916298 1.303225 1.314938
0.942478 1.376382 1.389483
0.968658 1.455009 1.468312
0.994838 1.539865 1.551587
1.021018 1.631852 1.639456
1.047198 1.732051 1.732051
0.55
0.85
1.15
1.45
1.75
0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05
f(x)
g(x)
5ª Questão
x f(x) g(x)
-2.000000 32.000000 32.000000
-1.750000 23.816406 25.750000
-1.500000 17.812500 20.000000
-1.250000 13.378906 14.750000
-1.000000 10.000000 10.000000
-0.750000 7.253906 5.750000
-0.500000 4.812500 2.000000
-0.250000 2.441406 -1.250000
0.000000 0.000000 -4.000000
0.250000 -2.558594 -6.250000
0.500000 -5.187500 -8.000000
0.750000 -7.746094 -9.250000
1.000000 -10.000000 -10.000000
1.250000 -11.621094 -10.250000
1.500000 -12.187500 -10.000000
1.750000 -11.183594 -9.250000
2.000000 -8.000000 -8.000000
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
f(x)
g(x)
7ª Questão h1= 0.1
x(rad) Y(x) (Euler) y´(x) Analítico Ep(%)(Euler)
0.00000 1.000000 2.000000 1.000000 0.000E+0
0.10000 1.200000 1.995004 1.199833 1.392E-2
0.20000 1.399500 1.980067 1.398669 5.941E-2
0.30000 1.597507 1.955336 1.595520 1.245E-1
0.40000 1.793041 1.921061 1.789418 2.025E-1
0.50000 1.985147 1.877583 1.979426 2.890E-1
8ª Questão
x(rad) Y(x)(RK2) K1 K2 Analítico Ep(%)(RK2)
0.00000 1.000000 2.000000 1.995004 1.000000 0.000E+0
0.10000 1.199750 1.995004 1.980067 1.199833 6.918E-3
0.20000 1.398504 1.980067 1.955336 1.398669 1.180E-2
0.30000 1.595274 1.955336 1.921061 1.595520 1.542E-2
0.40000 1.789094 1.921061 1.877583 1.789418 1.811E-2
0.50000 1.979026 1.877583 1.825336 1.979426 2.021E-2
9ª Questão h2= 0.100000
x(rad) Y(x) (Euler) y´(x) Analítico Ep(%)(Euler)
0.00000 4.000000 1.000000 4.000000 0.000E+0
0.10000 4.100000 1.305171 4.115171 3.687E-1
0.20000 4.230517 1.621403 4.261403 7.248E-1
0.30000 4.392657 1.949859 4.439859 1.063E+0
0.40000 4.587643 2.291825 4.651825 1.380E+0
0.50000 4.816826 2.648721 4.898721 1.672E+0
10ª Questão
x(rad) Y(x)(RK2) K1 K2 Analítico Ep(%)(RK2)
0.00000 4.000000 1.000000 1.305171 4.000000 0.000E+0
0.10000 4.115259 1.305171 1.621403 4.115171 2.138E-3
0.20000 4.261588 1.621403 1.949859 4.261403 4.341E-3
0.30000 4.440151 1.949859 2.291825 4.439859 6.577E-3
0.40000 4.652235 2.291825 2.648721 4.651825 8.814E-3
0.50000 4.899262 2.648721 3.022119 4.898721 1.104E-2
11ª Questão h3= 0.100000
x(rad) Y(x) (Euler) y´(x) Analítico Ep(%)(Euler)
0.00000 2.000000 -1.000000 2.000000 0.000E+0
0.10000 1.900000 -0.700000 1.914512 7.580E-1
0.20000 1.830000 -0.430000 1.856192 1.411E+0
0.30000 1.787000 -0.187000 1.822455 1.945E+0
0.40000 1.768300 0.031700 1.810960 2.356E+0
0.50000 1.771470 0.228530 1.819592 2.645E+0
12ª Questão
x(rad) Y(x)(RK2) K1 K2 Analítico Ep(%)(RK2)
0.00000 2.000000 -1.000000 -0.700000 2.000000 0.000E+0
0.10000 1.915000 -0.715000 -0.443500 1.914512 2.549E-2
0.20000 1.857075 -0.457075 -0.211368 1.856192 4.757E-2
0.30000 1.823653 -0.223653 -0.001288 1.822455 6.574E-2
0.40000 1.812406 -0.012406 0.188835 1.810960 7.985E-2
0.50000 1.821227 0.178773 0.360896 1.819592 8.986E-2
Questões 7 e 8
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.0 0.1 0.2 0.3 0.4 0.5
Ep(%)(Euler)
Ep(%)(RK2)
Questões 9 e 10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.0 0.1 0.2 0.3 0.4 0.5
Ep(%)(Euler)
Ep(%)(RK2)
Questões 11 e 12
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.1 0.2 0.3 0.4 0.5
Ep(%)(Euler)
Ep(%)(RK2)