eulers improved method code error

6 visualizaciones (últimos 30 días)
Syed Haque
Syed Haque el 14 de Oct. de 2019
Comentada: Syed Haque el 17 de Oct. de 2019
tried to solve ode using eulers improved method for a function of F=2xy
with step size h=0.1,y0=1,x0=1 and seeking y(1.5)
The code is as follows
function yout=improvedeuler3(F,x0,h,xfinal,y0);
y=y0;
yout=y;
for x=x0:h:xfinal-h;
s1=F(x,y);
s2=F(x+h/2,y+h*s1/2); %% is it correct for modified euler
y=y+h*s2;
yout=[yout,y];
end
end
initial conditions and conecting script is
F=@(x,y)2*x*y;
x0=1;
h=0.1;
xfinal=1.5;
y0=1;
yout=improvedeuler(F,x0,h,xfinal,y0);
%comparision with exact
x=x0:h:xfinal;
y_exact=exp((x.^2)-1);
plot(x,yout,'r',x,y_exact,'k'),legend('Improved','Exact');
I am getting a matlab output of y values different from that calculated manually
It seems there is an error in the code,unable to makeout.
1 1.2310 1.5452 1.9779 2.5814 3.4348 ------ matlaboutput
1 1.2320 1.5479 1.9832 2.5908 3.4509 ------ manual calculation
  3 comentarios
Syed Haque
Syed Haque el 15 de Oct. de 2019
1 1.205 1.4754 1.8352 2.3193 2.9776 with h=0.09
1 1.231 1.5453 1.978 2.5814 3.4348 with h=0.10
1 1.2576 1.6193 2.1345 2.88 with h=0.11 (y1.5 with this step is missing)
something wrong with the code
darova
darova el 15 de Oct. de 2019
Looks good as for me. What do you think?
img1.png

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Respuesta aceptada

James Tursa
James Tursa el 15 de Oct. de 2019
Editada: James Tursa el 15 de Oct. de 2019
s2=F(x+h/2,y+h*s1/2); %% is it correct for modified euler
If "Improved" Euler's Method means "Modified" Euler's Method as your comment indicates, then no it is not correct.
Modified Euler is basically finding the derivative at the current point, finding the derivative one full step ahead of the current point, and then using the average of the two derivatives to make your integration step. So this:
s1=F(x,y);
s2=F(x+h/2,y+h*s1/2); %% is it correct for modified euler
y=y+h*s2;
should look something like this instead (inserting spaces for reading clarity):
s1 = F(x , y ); % derivative at current point
s2 = F(x+h, y+h*s1); % derivative at one full step ahead (using predicted point from standard Euler Method)
y = y + h*(s1 + s2)/2; % integrate forward using the average of the two derivatives
Did you really mean to use the "Midpoint" Method? What is the actual assignment you were given?
  2 comentarios
Syed Haque
Syed Haque el 15 de Oct. de 2019
Getting an error,assignment is to calculate y1.5 and compare error at all points upto 1.5 with actual.
James Tursa
James Tursa el 15 de Oct. de 2019
Can you post your current code and the assignment text? Many contributors here (myself included) are not willing to open active documents like Excel or Word etc.

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Más respuestas (1)

Syed Haque
Syed Haque el 16 de Oct. de 2019
function yout=improveuler(F,x0,h,xfinal,y0);
y=y0;
yout=y;
for x=x0:h:xfinal-h;
s1=F(x,y);
s2=F(x+h,y+h*s1);
y=y+h*(s1+s2)/2;
yout=[yout,y];
end
end
F=@(x,y)2*x*y;
x0=1;
h=0.1;
xfinal=1.5;
y0=1;
yout=improveuler(F,x0,h,xfinal,y0);
%comparision with exact
x=x0:h:xfinal;
y_exact=exp((x.^2)-1);
plot(x,yout,'r',x,y_exact,'k'),legend('Improved','Exact');
% COMMAND WINDOW ERROR PROMPT
>> improveuler
Not enough input arguments.
Error in improveuler (line 2)
y=y0;
develop improved euler method to solve y1.5 given y'=2xy, y1=1
  3 comentarios
James Tursa
James Tursa el 16 de Oct. de 2019
Same for me. When I put this code in a file called improveuler.m
function yout=improveuler(F,x0,h,xfinal,y0);
y=y0;
yout=y;
for x=x0:h:xfinal-h;
s1=F(x,y);
s2=F(x+h,y+h*s1);
y=y+h*(s1+s2)/2;
yout=[yout,y];
end
end
and this code in a separate file called improveuler_test.m
F=@(x,y)2*x*y;
x0=1;
h=0.1;
xfinal=1.5;
y0=1;
yout=improveuler(F,x0,h,xfinal,y0);
%comparision with exact
x=x0:h:xfinal;
y_exact=exp((x.^2)-1);
plot(x,yout,'r',x,y_exact,'k'),legend('Improved','Exact');
and then type the following at the command line
improveuler_test
I get it to run without errors and produce what looks like a reasonable plot.
Syed Haque
Syed Haque el 17 de Oct. de 2019
Thanks James,could finally achieve the end result,y values are matching with calculated ones.seems all those multiple files of the same assignment was playing havoc,deleted them,pasted the script again from the forum(debugging cropped up-shouldn't have done that) and finally after three/four hits I could see the code run successfully.
Also sorry for posting earlier comment as an answer.

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