Questions tagged [pde]
Partial differential equations (PDEs) are equations that relate the partial derivatives of a function of more than one variable. This tag is intended for questions on modeling phenomena with PDEs, solving PDEs, and other related aspects.
895
questions
1
vote
0
answers
107
views
How to implement boundary conditions for the Thomas algorithm
For my variable $U(t,x)$, I have implemented the thomas algorithm with $U_j^i$:
$$ a(x)U_{j-1}^{i+1}+ b(x)U_j^{i+1} + c(x)U_{j+1}^{i+1} = d(x)U_j^{i} $$
Then $\textbf{A}$ is a tridiagonal vector with ...
0
votes
0
answers
53
views
Prof A. Stanoyevitch's finite difference based PDE matlab code
Where can one find Prof A. Stanoyevitch's finite difference based PDE matlab code? They have a book on such a topic but can't find the accompanying code.
Is it well received? It's not commonly talked ...
0
votes
1
answer
95
views
Prof Lawrence Shampine's hpde matlab code
Where can one find Prof Lawrence Shampine's hpde matlab code?
Is it well received? It's not commonly talked about.
2
votes
0
answers
57
views
Why the following discrete inequality are equal?
When reviewing papers on the numerical solutions of Partial Differential Equations (PDEs), I observed the following equation:
$$
(1-C\tau)||\theta^n||^2 \leq ||\theta^{n-1}||^2 + C\tau (h^{2r+2}),
$$
...
1
vote
0
answers
84
views
Seeking open-source PDE Solver for inhomogeneous material properties
I'm currently in search of an open-source PDE solver (Finite Element Method is preferred) that can effectively handle the challenge of material properties coefficients associated with each element in ...
2
votes
1
answer
304
views
Literature request covering Chebyshev's pseudospectral collocation method
I would like to request some literature recommendations covering Chebyshev's pseudospectral collocation method for solving space-time PDEs. It would be nice if it even contained some example problems ...
0
votes
0
answers
59
views
Solving AU = F using linalg.cg results in 0 iterations
I am working on solving the following PDE: $$\left(\mu_{x}\frac{\partial^{2}u}{\partial x^{2}}+\mu_{y}\frac{\partial^{2}u}{\partial y^{2}}\right)=f(x,y) \tag 1$$
Which is then discretised:
$$- \mu_{x} ...
0
votes
0
answers
109
views
Solving a steady-state PDE
I'm working on trying to solve a steady state PDE in python and I am quite new to python and I am slightly confused on the implementation details. I have an example implementation of solving a non-...
4
votes
1
answer
148
views
Burger's equation (PDE) does not work with downwind difference?
I'm working on implementing the discretised Burger's equation. I am quite confused as to why it does not work when using a step-function and downwind difference formula. When using a step-function and ...
1
vote
1
answer
155
views
Finite Difference method, ADI Scheme of Douglas and Rachford
I am trying to implement the ADI scheme of Douglas and Rachford.
For $p(X,Z,t)$, there is:
$$
\begin{gathered}
A=p^{n-1}+\Delta t_n\left[F_0\left(p^{n-1}, t_{n-1}\right)+F_1\left(p^{n-1}, t_{n-1}\...
4
votes
0
answers
126
views
FVM for non-regular domain with triangular mesh
Setup
The 1D convection-diffusion equation is given by:
\begin{equation}\tag{1}
\frac{\partial u}{\partial t} + v \frac{\partial u}{\partial x} - \mu \frac{\partial^2 u}{\partial x^2} = 0,
\end{...
0
votes
0
answers
48
views
Is a sort of "z-drift" the result of numerical precision errors in FDM?
Upon solving the 2D wave equation with Neumann boundary conditions $u_x = u_y = 0$ on a rectangular $10 \times 10 \times 10$ grid, I noticed something odd - $u$ seemed to shift upwards with time. This ...
1
vote
0
answers
44
views
Solution to the Liouville-Gibbs equation
What would be the approach to numerically solve for $\rho(x,t)$ the following equation with some initial conditions
$$\frac{\partial\rho}{\partial t}
+\sum_{i=1}^n\left(\frac{\partial(\rho g_i)}{\...
0
votes
1
answer
68
views
Local truncation error of given implicit 1-step scheme
I'm given the 1-step implicit scheme $$y_{n+1} = y_n + \frac{h}{6}[4f(t_n, y_n) + 2f(t_{n+1}, y_{n+1}) + hf'(t_n, y_n)],$$
where $y'(t) = f(t, y)$, and I'm seeking the scheme's local truncation error. ...
0
votes
0
answers
64
views
How to set Neumann BC for coupled transport problem in weak form?
Consider
$$\begin{aligned}
\partial_t v + b\cdot \nabla \phi &=0 \\
\partial_t \phi + b\cdot \nabla v &= 0
\end{aligned}$$
for $v:(x,y)\mapsto \mathbb{R}$, unknown and time-dependent ($...