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.
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How can I get more accurate electric scalar potential in 2D closed box?
I am trying to use poisson equation to plot the electric scalar potential in close 2D space. The details in in this video
and this one
The following in written in Matlab for quick prototype.
...
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Asking advice for implementation of Conservative Finite Difference Scheme for numerically solving Gross-Pitaevskii equation
I am trying to numerically solve the Gross-Pitaevskii equation for an impurity coupled with a one-dimensional weakly-interacting bosonic bath, given by (in dimensionless units):
\begin{align}
i \frac{\...
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What is the best finite volume method for the following equation?
I'm trying to create a partial differential equation that approximates 1-D climate in a rocky planet's atmosphere, which accounts for energy transport via radiation and convection. I am only ...
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How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?
I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
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How to constraint the tangential gradient on a boundary in FEniCS?
The problem I'm considering is a 2D scalar PDE.
The domain $\Omega$ is a disk with two holes $\partial\Omega_1$ and $\partial\Omega_2$ and an external boundary $\partial\Omega_0$.
The PDE and boundary ...
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How to obtain the transfer function between boundary condition and point of wave equation?
I am considering the wave equation with position varying material properties
$$
m(x) \frac{\partial^2 u}{\partial t^2} = \frac{\partial}{\partial x}\left(k(x) \frac{\partial u}{\partial x}\right), \...
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Numerically solving the Advection-diffusion equation with no-flux boundary condition leads to violation of mass conservation
I am trying to solve numerically the advection-diffusion equation of the following form
$$\frac{\partial C}{\partial t}=\alpha\frac{\partial^2 C}{\partial x^2}+\beta \frac{\partial C}{\partial x}$$
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Vector poisson equation in cylindrical coordinates. What's wrong?
I am trying to solve this equation:
$$
\frac{\partial^2 A}{\partial r^2} + \frac{1}{r}\frac{\partial A}{\partial r} - \frac{A}{r^2} + \frac{\partial^2 A}{\partial z^2} = -g
$$
This is basically the ...
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Which class of PDEs is well-suited for multistep methods?
I am experimenting with machine learning techniques to solve partial differential equations (PDEs). My goal is to use solutions from previous time steps to predict the solution at the next time step, ...
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How to refine $h$ and $\Delta t$ for convergence tests on evolution PDE
Setting
I am solving for $u(x,y,t)$ the wave equation $\partial_{tt} u - \partial_{xx} u = f$ on $(x,y)\in\Omega=[0,1]\times \mathbb{R}$ by splitting it into an equivalent first order system:
$$\...
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Iterative PDE solver for 1D Burgers equation
I am looking for an Iterative Numerical PDE solver for 1D Burgers equation. I need to have access to the intermediate solutions of the Numerical Solver. By iterative methods, I mean techniques which ...
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Boundary conditions of a 2D explosion case
I want to solve this problem explosion test case. I was wondering about what are usual the boundary conditions for this type of problems. I want the wave to bounce of the boundary of the domain (let's ...
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Monotonicity of Errors with Respect to Step Sizes in Numerical Methods for PDEs
Consider a non-linear partial differential equation (PDE) (e.g., Burgers' equation) that is solved numerically using a finite difference method (or a similar approach). Suppose a grid search is ...
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numerical schemes for 1D PDE: for smaller grid size there is an increased roundoff error, larger size more truncation, so sweet spot in between?
I had a discussion with a colleague today. He claimed that usually for a general numerical scheme for solving a general 1D PDE, for smaller grid size there is an increased roundoff error because of ...
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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}\...
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