I wonder exactly in what situation we would prefer one method to combat instability over another? Are there any examples?
tiffanysun1
@lycorisradiatu
I believe the choice of method to combat instability is pretty context-dependent. For example, the Modified Euler method might be preferred for its simplicity and improved accuracy over the standard Euler method without too much additional computational cost. Adaptive step size is useful when dealing with systems where the solution changes rapidly or unpredictably, as it adjusts the step size to maintain accuracy. Implicit methods, while computationally intensive, are often used in stiff systems where other methods fail to maintain stability.
omijimo
though this is similar to adaptive step size, would it be possible to sort of implement supersampling, as in running the simulation N times as averaging the result? would this lead to the overall most accurate simulation?
I wonder exactly in what situation we would prefer one method to combat instability over another? Are there any examples?
@lycorisradiatu I believe the choice of method to combat instability is pretty context-dependent. For example, the Modified Euler method might be preferred for its simplicity and improved accuracy over the standard Euler method without too much additional computational cost. Adaptive step size is useful when dealing with systems where the solution changes rapidly or unpredictably, as it adjusts the step size to maintain accuracy. Implicit methods, while computationally intensive, are often used in stiff systems where other methods fail to maintain stability.
though this is similar to adaptive step size, would it be possible to sort of implement supersampling, as in running the simulation N times as averaging the result? would this lead to the overall most accurate simulation?