Does this implicit Euler Method imply the existence of an EXPLICIT Euler Method and if so, what advantages/disadvantages does each offer over the other?
SudhanvaKulkarni123
To answer AXM's question - yes EXPLICIT Euler is just the vanilla Euler from earlier on in the slides. The pros and cons are roughly that explicit Euler is very easy to implement and cheap but you lose stability. Implicit Euler on the other hand requires you to use a non-linear solver like Newton's which makes it harder to implement and more expensive - but we are able to enjoy stability.
CLV-Iclucia
If the system is stiff, it would require a
very small step size to make the explicit solvers stable. But for implicit solvers you cna use a much larger time step.
Does this implicit Euler Method imply the existence of an EXPLICIT Euler Method and if so, what advantages/disadvantages does each offer over the other?
To answer AXM's question - yes EXPLICIT Euler is just the vanilla Euler from earlier on in the slides. The pros and cons are roughly that explicit Euler is very easy to implement and cheap but you lose stability. Implicit Euler on the other hand requires you to use a non-linear solver like Newton's which makes it harder to implement and more expensive - but we are able to enjoy stability.
If the system is stiff, it would require a very small step size to make the explicit solvers stable. But for implicit solvers you cna use a much larger time step.