All Questions
Tagged with crank-nicolson differential-equations
4
questions
0
votes
2
answers
417
views
Can the Crank-Nicolson Method Be used to Solve The Schrodinger Equation with a Time Varying Potential?
I have been following an excellent article about how to use the Crank-Nicolson method to solve the Schrodinger equation. In the article, it starts with a $V(x, y, t)$ but the potential seems to become ...
2
votes
0
answers
86
views
Linearising Nonlinear Coupled Partial Differential Equations - Alfvénic Diffusion
I am trying to solve the following coupled partial differential equations with a finite difference scheme:
$$\partial_tf+v\partial_zf+\partial_z\frac{1}{W}\partial_zf=0$$
$$\partial_tW+v\partial_zW-\...
1
vote
1
answer
323
views
Crank-Nicholson for diffusion-advection vs diffusion equation
Let's consider the following 1D diffusion equation:
$\frac{\partial u}{\partial t} = xk \frac{\partial}{\partial x}(\frac{1}{x}\frac{\partial u}{\partial x})$
where we assume that the diffusion ...
0
votes
1
answer
1k
views
Crank–Nicolson method for nonlinear differential equation
I want to solve the following differential equation from a paper with the boundary condition:
The paper used the Crank–Nicolson method for solving it. I think I understand the method after googling ...