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# Tag Info

## Hot answers tagged implicit-methods

Accepted

### Are stiffness and instability equivalent?

There are non-stiff problems which are unconditionally unstable with some explicit methods, and conversely there are stiff problems which can be stable with explicit methods. Consider the oscillating ...
• 2,794
Accepted

### Solving PDE implicitly or explicitly depending on stiffness

If you just slap together an implicit and an explicit method you will likely have order loss. You can do so with low order methods though, and Crank-Nicholson mixed with some other integrator is an ...
• 12.3k
Accepted

### Stiff ODE solver in the web browser

I am the author of diffeq-js (https://github.com/martinjrobins/diffeq-js), which is a javascript library for solving DAE (and ODE) models in the browser using ...
Accepted

### Does this second-order implicit Runge-Kutta method have a name?

As Wolfgang stated in the comments, this is not a traditional RK due to the inconsistent time evaluations within a stage. At first it would seem it can't even be cast as an additive RK since terms ...
• 1,114

### Are stiffness and instability equivalent?

I'd like to add a few complements to the accepted answer. Some problems possessing some eigenvalues with positive real parts have "physically" unstable modes, which may actually be damped by ...
• 1,943
Accepted

### GMRES vs Newton-GMRES for Solving nonlinear PDE's

The reason is that GMRES can only be used for solving linear equations, i.e. equations of the form $Ax=b$, where $A$ is some matrix and $x,b$ are vectors. What GMRES does, essentially, is it ...
• 106
Accepted

### Textbook/Manual on Implicit FEM Methods

I think you're mixing up ideas. The best thing here is to know the foundations, and it then "implicit FEM" will be a trivial idea (which is why there won't be a book specifically about that). Finite ...
• 12.3k
Accepted

### Solve an ODE with positivity-preserving property unconditionally

The two properties are usually called positivity-preserving and monotonicity-preserving (makes it easier to find this question). Looking at http://www.ams.org/journals/mcom/2006-75-254/S0025-5718-05-...
• 11.4k
Accepted

• 6,109
1 vote

### Finite difference - Explicit / Implicit / Crank Nicolson - Does the implicit method require the least memory?

You seem to have given the 1D equations for the discretizations, even though the problem is in 2D. Regardless, the explicit method requires the least memory since you don't even have to form a ...
• 343
1 vote

### Solving a PDE implicitly by iteration in python

To answer your questions: Is there any better way to do it without being able to use matrix notation? Yes, there are alternative ways, but this is not the best approach. In other words, this method (...
1 vote

### Implicit solution to Sylvester equation

Yes, there is active research on that, especially in the Lyapunov case: it turns out under some conditions $M$ is well approximated by a low-rank or banded matrix. So you can find an implicit ...
• 11.4k
1 vote
Accepted

• 305
1 vote

### Textbook/Manual on Implicit FEM Methods

The implicit/explicit designation refers to the finite difference time stepping scheme used to compute dynamic models. Nonlinear Finite Element Methods by Peter Wriggers talks about the two different ...
• 11
1 vote

### CFD: Doubt with time convergence in advection fully implicit upwind scheme

You can take a look at the truncation errors in your discretization. For example, for your time discretization, the truncation error would be $$\frac{\Delta t}{2} \frac{\partial^2 T}{\partial t^2}$$...
• 23

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