Improve Mathworks Euler method

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.

Answer 1

[Alan Stevens]

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).

[Alan Stevens]

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 ');

 x1        y1   x2        y2 

fprintf('\n%4.3f  %4.3f   %4.3f  %4.3f ',x1(end),y1(end),x2(end),y2(end));

9.800  47.040   9.800  -435.001 

figure(1);
plot(x1,y1), grid

figure(2)
plot(x2,y2),grid

[Alan Stevens]

Yes, they will both appear on one graph that way.