This method makes a lot of sense. While Euler's method may seem much more simple and faster to compute at each step, there is a potential for instability. If there is any instability, the algorithm could fail. This is a risk that we cannot afford to take, so using the adaptive step size method is a must to ensure reliability
AnikethPrasad
I agree, being able to dynamically adjust the step size based on the behavior helps create more accurate and dependable results when running simulations.
aishikbhattacharyya
This method does a good job at preventing places where the graph might peak significantly and cause the error to affect to the result too much. Now with a step size, the result can be more stable.
kalebdawit
The key drawback of this method is that it can be expensive when we need very small steps to maintain stability. Are there techniques to reduce the cost of trying many different step sizes by optimizing the choice of initial test step size? I imagine that there might be a way to choose a small enough initial step size (based on certain properties of our goal trajectory) so that we don't have to try out many step sizes before finding one that doesn't blow up.
rishiskhare
Overshooting by reducing the step size between time steps seems very intuitive, but I wonder how the perturbation applied to step size is determined (i.e. how much we deduce the step size between iterations). To me, it seems that some sort of gradient calculate might help in this adaptive technique, though maybe it's just a matter of iterative trial-and-error.
This method makes a lot of sense. While Euler's method may seem much more simple and faster to compute at each step, there is a potential for instability. If there is any instability, the algorithm could fail. This is a risk that we cannot afford to take, so using the adaptive step size method is a must to ensure reliability
I agree, being able to dynamically adjust the step size based on the behavior helps create more accurate and dependable results when running simulations.
This method does a good job at preventing places where the graph might peak significantly and cause the error to affect to the result too much. Now with a step size, the result can be more stable.
The key drawback of this method is that it can be expensive when we need very small steps to maintain stability. Are there techniques to reduce the cost of trying many different step sizes by optimizing the choice of initial test step size? I imagine that there might be a way to choose a small enough initial step size (based on certain properties of our goal trajectory) so that we don't have to try out many step sizes before finding one that doesn't blow up.
Overshooting by reducing the step size between time steps seems very intuitive, but I wonder how the perturbation applied to step size is determined (i.e. how much we deduce the step size between iterations). To me, it seems that some sort of gradient calculate might help in this adaptive technique, though maybe it's just a matter of iterative trial-and-error.