无法识别的 function 或变量“x”。 在 matlab

Question

trying to write Matlab code to implement Euler's Method to solve the differential equation y'=2+2x-x2 subject to initial condition y(0)=1. Please use step size 0.1 and estimate the value at x=1 and x=2.

when i run the code i get Unrecognized function or variable 'x'

dy =(2+2*x-2^2);

  x0 = 1;


  xn = 2;


  y = 1;

  h = 0.1;

  fprintf ('x \t\t y (Euler)\t y (analytical)\n') %data table header 

  fprintf ('%f \t %f\t %f\n' ,x0,y,(x0));


  for x = x0 : h : xn-hypot

   y= y + 2+2*x-2^2 * h;


  x = x + h;


  fprintf ('%f \t %f\t %f\n',x,y,(x));

 end

Answer 1

The problem is on the first line of the code:

dy =(2+2*x-2^2);

as this is the first statement of the code, the variable x has not been declared and Matlab returns the error you provided.

I would like also to add two comments:

1. Because in the for loop you already typed in the derivative, y= y + 2+2*x-2^2 * h; , you do not need to state the derivative in the beginning of the code. Either comment or delete the first line.

2. However, a better approach to make the Euler Method a little more general, is to use function handles . Then you can type in the first line of the code

   dy = @(x) (2+2*x-2^2);

and in the for loop use this function:

for x = x0 : h : xn-hypot
   y = y + dy(x) * h;
   x = x + h;
end

This way, you do not need to change your for loop with the Euler method, and it actually works for any first order differential equation (just change the dy function).