# Tag Info

Accepted

Accepted

### Why is Crank-Nicolson considered implicit in time?

A simplification - the Crank-Nicolson method uses the average of the forward and backward Euler methods. The backward Euler method is implicit, so Crank-Nicolson, having this as one of its ...

Accepted

### Numerical solution of burgers equation with finite volume method and crank-nicolson

If I understand correctly, you are using a centered finite difference in space and the implicit trapezoidal method in time. That scheme is unconditionally absolutely stable, but will generate ...
Accepted

### Derivation of a parabolic PDE using Alternating Direction Implicit method

Yes, this is correct in the sense that it is second order in both time and space. It is not the only way to handle the $f(x, y, t)$ term, however. From the equations you wrote, it appears that the ...
Accepted

1 vote

### Stability of Crank-Nicolson for $u_t = iu_{xx}+2iu$

The scheme is indeed unstable. It explodes - but very very slowly. By printing the maximum eigenvalue of the operator i confirmed the instability. It's greater than 1. Then why does it work? because ...
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 ...
1 vote
Accepted

### Finite Differencing schemes for Convection-Diffusion equation

it is ok for the discretization. CD scheme has some stability problem when Pe>2, but we can decrease the mesh spacing to obtain a low mesh Pe number. QUICK-scheme is more stable and accurate than CD, ...
1 vote

### Solving an equation in space and time using the Crank-Nicolson approach

This question is confusing. At first you are speaking of a steady-state equation, and suddenly you speak of a time scale... I will try to clarify the following. From the numerical PDEs standpoint, ...
1 vote

### Is this system of diffusion equations well-posed?

I was curious about your problem and it was not difficult for me to test CN method for your two equations. Added - parts beginning with "added" were written afterwards to address the comment. The ...

Only top scored, non community-wiki answers of a minimum length are eligible