Linked Questions

18 votes
5 answers
3k views

periodic boundary conditions and NDEigensystem

Mathematica 10 has a splendid new function, NDEigensystem, that makes it possible to solve Sturm-Liouville problems numerically in a single step. I have not however been able to find a way to get it ...
Leon Avery's user avatar
  • 1,342
12 votes
4 answers
1k views

Solving Burger's equation with NDSolve at large time

I want to solve the following Burger's equation $$\partial_tu+\partial_x\left(\frac{u^2}{2}\right)=0,~~x\in[0,2\pi],~t>0\\u(x,0)=\frac{1}{3}+\frac{2}{3}\sin(x)$$ with mathematica. Here's my code: <...
Ho-Oh's user avatar
  • 245
16 votes
3 answers
4k views

Solve Laplace equation in Cylindrical - Polar Coordinates

Hey mathematica stackexchange!! I've got a (possibly stupid) problem. I've tried many things to no avail, and I've read every post I've found on Laplace's equation. Background: I'm trying to find the ...
Peanut14's user avatar
  • 365
6 votes
2 answers
399 views

NDSolve for Laplace equation on disk is not working

I want to solve the laplace equation on the disk using NDSolve. Particularly I want to solve the problem $$\frac{\partial^2 u }{\partial r^2 } +r^{-1}\frac{\partial u }{\partial r }+r^{-2}\frac{\...
paradox's user avatar
  • 173
7 votes
1 answer
431 views

Problems with DSolve and NDSolve for Dirichlet problem on an annulus

To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro ...
user64494's user avatar
  • 26.8k
5 votes
2 answers
418 views

FEM 2D mesh with inclusion

I want to create a FEM mesh with an inclusion, but I want to define the coordinates of the edge nodes manually, since I need the nodes for a problem that requires periodic boundary conditions. The ...
Max's user avatar
  • 634
5 votes
2 answers
656 views

Solving PDE with Dirichlet, Neumann and Boundary conditions

I am trying to solve the following PDE: $$ u_{xx} + u_{yy} = \begin{cases} - \cos(x) \quad -\pi/2 \leq x \leq \pi/2, \\ 0 \quad \text{otherwise} \end{cases} $$ The domain is $\Omega = [-\pi,\pi] \...
user82261's user avatar
  • 151
10 votes
1 answer
403 views

FiniteElement v.s. TensorProductGrid: which is reliable for Schrödinger equation with periodic b.c.?

This is a problem comes up in the discussion under this post and I think it's worth starting a new question for it. I suspect the underlying issue is the same as in this post, but not sure. Consider ...
xzczd's user avatar
  • 66.9k
2 votes
1 answer
434 views

Discontinuity problem with 3D cylindrical heat equation (possibly due to a conversion between Cartesian to Cylindrical coordinates)

I have been working a certain type of 3D cylindrical diffusion equation for a bit now. I am trying to simulate a longitudinal diffusion process in a cylinder with a dislocation defect that will make ...
ConfuzzledStudent's user avatar
6 votes
1 answer
451 views

FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
SantaP's user avatar
  • 845
0 votes
1 answer
217 views

Laplace equation with mixed partial

I would like to solve numerically a modified Laplace PDE (with source terms) and which have a second-order mixed partial derivative, and is limited to the following region and periodic boundary ...
SAC's user avatar
  • 1,335
3 votes
2 answers
168 views

Error in definition of PeriodicBoundaryCondition?

The documentation for PeriodicBoundaryCondition (https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html) has: Where it says $u ( x_{target} ) = a + b\ u ( f ( x_{target} ) )$, I ...
Anthony's user avatar
  • 87
1 vote
1 answer
246 views

How to solve a reaction-diffusion?

I would like to solve a PDE system reaction-diffusion type (2D spatial + 1 temporal) coupled as described below. Another question of this same system was solved here: System of nonlinear PDE 2D (...
SAC's user avatar
  • 1,335
3 votes
0 answers
415 views

Problem computing a cylindrical Heat equation with a parameter alpha

i have been struggling to compute a particular instance of cylindrical 3D heat equation. Here is my code : ...
ConfuzzledStudent's user avatar
0 votes
0 answers
42 views

PDE Problem: NDsolve give the results inconsistent with the initial state [duplicate]

We are solving the non-linear PDE, like this ...
so_sure's user avatar
  • 351