Improve Mathworks Euler method
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Hi, I'm newbi to MATLAB, but I am writing code based on this example: https://www.mathworks.com/matlabcentral/fileexchange/72522-euler-method. I wrote code that is compiled and there is output on it but I don't know how to check it properly. I would be very grateful if someone would take a look.
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Answers (1)
Alan Stevens
on 25 Apr 2021
The method is ok, though could be more streamlined, for example:
f1=@(x) 5*x+50;
f2 =@(x,y) x*10 +10*y;
x1=0;
y1=0;
x2=0;
y2= 0;
xn=10;
h=0.2;
n = round(xn/h);
for i = 1:n
y1=y1+h*f1(x1);
x1=x1+h;
y2=y2+h*f2(x2,y2);
x2=x2+h;
end
fprintf('\n x1 y1 x2 y2 ');
fprintf('\n%4.3f %4.3f %4.3f %4.3f ',x1,y1,x2,y2);
Your functions (especially f2) show up the deficiencies in the Euler method (the true final value at x = 10, for f1 is 750, and for f2 is ~2.688*10^42).
2 Comments
Alan Stevens
on 25 Apr 2021
More like this (note: I altered your value of D to give more reasonable results):
A = 5;
B = 50;
C = 0.1;
D=1;
f1=@(x) (1./D)*x;
f2 =@(x,y) (1./D)*(A-(B*x)-y);
x1(1)=0;
y1(1)=0;
x2(1)=0;
y2(1)= 0;
xn=10;
h=0.2;
n = round(xn/h);
for i = 1:n-1
y1(i+1)=y1(i)+h*f1(x1(i));
x1(i+1)=x1(i)+h;
y2(i+1)=y2(i)+h*f2(x2(i),y2(i));
x2(i+1)=x2(i)+h;
end
fprintf('\n x1 y1 x2 y2 ');
fprintf('\n%4.3f %4.3f %4.3f %4.3f ',x1(end),y1(end),x2(end),y2(end));
figure(1);
plot(x1,y1), grid
figure(2)
plot(x2,y2),grid
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