0

I don't quite understand the discretisation error of Euler's method

$$L(t,h)=\frac{x(t+h)-x(t)}{h}-f(t,x(t))$$

What I don't understand is: $\frac{x(t+h)-x(t)}{h}$ is the "gradient" and $f(t,x(t)$ is the value of the function. How can we get the error by subtracting the former by the latter?

Thanks.

user71346
  • 4,171

1 Answers1

1

You assume that $x(t)$ is an exact solution to $\dot x = f(t,x)$ and then apply Taylor formulas.

Lutz Lehmann
  • 126,666