Euler's Method Problem

Hi guys. In the task, it is necessary to calculate by the Euler method with the initial condition y(x0)=y0 , [a;b] wiith epsilon 0.001.

I have a function, but it only works correctly if y^1

For example, when f=x^(-2)*y^3 will be an error function S = sym(x, n, a) and the program stops

euler('x^(-2)*y^3',[1 2],[1 4], 50, 0.001)

Maybe you can help me? What could be the problem?

function [] = euler( f,X0,AB,n0,eps )
% f - original function
% X0 - coordinates of the starting point from the segment from which to start splitting
% A - segment [a; b]
% n0 - the initial number of partitions of the segment
% e - accuracy
 
 
x0=X0(1);
y0=X0(2);
a=AB(1);
b=AB(2);
 
 
% X() - array of abscissa values dx=(b-a)/n0
% Y() - array of ordinate values dx=(b-a)/n0
 
dx=(b-a)/n0; % the length of the split segment
X(1)=x0;
Y(1)=y0;
for i=1:1:n0
    syms x y
    y0=y0+subs(subs(f,x,x0),y,y0)*dx;
    x0=x0+dx;
    X(i+1)=x0;
    Y(i+1)=y0;
end
 
dx=dx/2; % reduce the length of the split segment by half
 
x0=X0(1);
y0=X0(2);
 
X1(1)=x0;
Y1(1)=y0;
% X1() - array of abscissa values dx=(b-a)/n0 * 0.5
% Y1() - array of ordinate values  dx=(b-a)/n0 * 0.5
for i=1:1:2*n0
    y0=y0+subs(subs(f,x,x0),y,y0)*dx;
    x0=x0+dx;
    X1(i+1)=x0;
    Y1(i+1)=y0;
end
 
maax=max(abs(Y-Y1(1:2:end))); 
Y1_=Y1; 
 
x0=X0(1);
y0=X0(2);
 
 
 
 figure(1)
 hold on
 grid on
 plot(X,Y,'r'); % graph for the first case
 plot(X1,Y1,'g'); % graph for the second case
 
 
 
m=0;
while (maax>eps) 
    m=m+1;
    dx=dx/2; 
    X2(1)=x0;
    Y2(1)=y0;
    n=(b-a)/dx;
    for i=1:1:n
         y0=y0+subs(subs(f,x,x0),y,y0)*dx;
         x0=x0+dx;
         X2(i+1)=x0;
         Y2(i+1)=y0;
     end
     maax=max(Y1_-Y2(1:2:end)); 
     Y1_=Y2;
end 
      if m==0
          fprintf('There is not enough accuracy for making 2 graphics\n');
      else
       plot(X2,Y2,'b');  
      end
      
      for i=2:n+1
          fprintf('x = %f\ty = %f\n',X2(i),Y2(i));
      end
      fprintf('It took %i pieces of fragmintation \n',n)
end

Answer 1

[Walter Roberson]

Since R2018b it has not been valid to use text symbolic expressions such as 'x^(-2)*y^3' for any operation except dsolve() [and that will be eliminated soon, if it has not been already.]

If you have text that represents a symbolic expression, you must not use str2sym() to convert it to symbolic expression.