# Numerical solution's evolution's dependance on timestep and the absolute time passed.

After solving a heat equation (1 space dimension and the time dimension) with a scheme, if I get different results at the same absolute points of time for different durations of the timestep, does it mean that I have made a mistake?

With my solution I've noticed that my solution settles after a certain amount of iterations (or so it seems), and hence by making the timestep however small I want, it seems like I can make my solution settle after however small amount of time. Am I necesserily making a mistake?

• Too vague sorry. What scheme are you using? What do you mean by "settle"? If your endpoints are at constant temperature solutions will settle to a time invariant solution (steady state) under any stable iteration scheme. Does settle mean steady state? Converging to a steady state after any finite time depending on the time step sounds odd though.
– Paul
Commented Apr 28, 2020 at 20:08
• @Paul Yes, i meant steady-state. I have the derivative equal 1 at the beginning and the value equal 1 at the end. So it should converge to the line $f(x)=x$ with time. You can see my problem here: math.stackexchange.com/questions/3552473/… . I will try to look for mistakes in my code. I'm not going to post it here since it's a mess. Commented Apr 28, 2020 at 20:12