All Questions
Tagged with crank-nicolson numerics
8
questions
0
votes
1
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182
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Using Crank-Nicolson to solve Non-Linear Schrödinger equation in Python
I aim to solve the (non-linear) Schrodinger equation using the Crank-Nicolson method in Python. Here are my two functions.
...
2
votes
0
answers
173
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Error in implementation of Crank-Nicolson method applied to 1D TDSE?
Some context, I've posted this question on physics SE and stack overflow. The former had nothing to offer, the latter had a great commenter that agreed with the phase looking off being one of the ...
6
votes
2
answers
389
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Is the diffusion equation with Neumann and Dirichlet BCs well-posed?
I am considering the following diffusion equation:
$$\frac{\partial f}{\partial t} = \frac{\partial}{\partial x}[D(x,t)\frac{\partial f}{\partial x}]$$
over a grid ...
- 171
2
votes
2
answers
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Stability of Crank-Nicolson for $u_t = iu_{xx}+2iu$
I want to use the Crank-Nicolson scheme to solve the equation
$$u_t = iu_{xx}+2iu$$
Here's the analysis: Suppose we make a grid, with $k = dt$ and $h = dx$, the usual notation, and also $u_j^n = u(...
- 139
2
votes
1
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4k
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Applying Neumann boundaries to Crank-Nicolson solution in python
Consider the heat equation
$$u_t = \kappa u_{xx}$$
with boundary conditions of
$$u(x,0)=0\\
u(0,t)=100\\
u(l,t)=0$$
Numerical analysis by pyton can be done with
...
- 131
0
votes
1
answer
1k
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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 ...
- 217
1
vote
1
answer
631
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How can I numericaly solve a convection-diffusion equation with a large diffusion term?
I want to numerically solve the advection-diffusion equation:
\begin{equation}
u_t(x,t) + cu_x(x,t) = v u_{xx}(x,t)
\end{equation}
for $x \in [0,1]$ and $t \geq 0$ subject to the boundary conditions ...
- 113
1
vote
1
answer
409
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Numerical Solution of non-linear diffusion equation using Finite Differencing
I'm trying to solve the following non-linear diffusion equation:
$$
\frac{\partial}{\partial t} u(x,t)= \frac{\partial^{2}}{\partial x^{2}}u(x,t)^{3}$$ $$ -1\leq x \leq1, t \geq 0
$$ with the boundary ...
- 113