Percent Error
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John
am 27 Mär. 2011
Kommentiert: Walter Roberson
am 15 Sep. 2022
Below is some coding I have calculating percent error of Euler's method however there has to be a more efficient way to input the matrices, I have found the first two step size errors by manually inputing the values but before I do the third (extremely long), there has to be a faster way. Any suggestions?
%%Analytical
simplify(dsolve('Dy=-x/y','y(0)=5','x'))
%%Numerical
f=@(x) (-x^2+25)^(1/2)
dydx=@(x,y) -(x/y);
[x1,y1]=eulode(dydx, [0 5],5,.5);
[x2,y2]=eulode(dydx,[0 5],5,.1);
[x3,y3]=eulode(dydx,[0 5],5,.01);
disp([x1,y1])
disp([x2,y2])
disp([x3,y3])
%%Percent Error
x1=0:.5:5;
x2=0:.1:5;
x3=0:.01:5;
analytical_step1= (-x1.^2+25).^(1/2)
analytical_step2=(-x2.^2+25).^(1/2);
analytical_step3=(-x3.^2+25).^(1/2);
numerical_1=[5.000 5.000 4.9500 4.8490 4.6943 4.4813 4.2024 3.8454 3.3903 2.8004 1.9970 ]
numerical_2=[5.0000 5.0000 4.9980 4.9940 4.9880 4.9800 4.9699 4.9579 4.9437 4.9276 4.9093 4.8889 4.8664 4.8418 4.8149 4.7858 4.7545 4.7208 4.6848 4.6464 4.6055 4.5621 4.5161 4.4673 4.4159 4.3615 4.3042 4.2438 4.1802 4.1132 4.0427 3.9685 3.8904 3.8081 3.7214 3.6301 3.5337 3.4318 3.3240 3.2096 3.0881 2.9586 2.8200 2.6711 2.5101 2.3348 2.1421 1.9273 1.6835 1.3984 1.0480];
Percent_Error1=abs((analytical_step1-numerical_1)/analytical_step1)*100%answer displayed in percent
Percent_Error2=abs((analytical_step2-numerical_2)/analytical_step2)*100%answer displayed in percent
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Akzeptierte Antwort
bym
am 28 Mär. 2011
Just use your definition of f to obtain all values at once (do not re-use variables like y1 etc):
Percent_Error1 = abs((y1-f(x1))./f(x1));
where x1 and y1 are outputs from your function eulode()
7 Kommentare
Walter Roberson
am 15 Sep. 2022
Disculpas, pero Google tiene problemas para traducir "MRD" y "PTMR"
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