14
votes
Accepted
Balanced flux in FEA using NeumanValue
Update (Steady-State Solution)
I think the fundamental issue is that you are over constraining your system. Whether you are solving the "heat equation" or not, your operator has the same ...
- 16.2k
13
votes
periodic boundary conditions and NDEigensystem
I think here is another way to do it. For this we use the low level FEM functions. First we have a utility function that converts a PDE specification to a discrete version.
...
- 39.1k
13
votes
Accepted
Reciprocating flow in a channel over a heated surface
We can solve this problem with method proposed on my page.
Solution1. We use nondimensional form of equations with scale d and $t_s = d^2/(k_f/(c_p \rho))$. We ...
- 42k
12
votes
Accepted
Laplace's equation in spherical coordinates with Neumann b.c
Two issues here.
First of all, you've chosen 100 to approximate Infinity, which is way too large in this case. Something like <...
- 63.8k
12
votes
Accepted
Why DSolve solution to this PDE does not match NDSolve solution?
The "Polar" coordinates programmed into Mathematica implicitly assume that the $\theta$ coordinate runs between -π and π, not between 0 and 2π as your ...
- 15k
11
votes
periodic boundary conditions and NDEigensystem
Periodic potentials and Bloch waves
This is a completely different approach, using functionality that was already present in Mathematica version 8. I'm posting this because it's quite robust and also ...
- 96.8k
11
votes
Mathematica vs. MATLAB: why am I getting different results for PDE with non-constant boundary condition?
As @Henrik Schumacher points out, you have a very high aspect ratio (1000:1) domain. It is always conducive to conduct a dimensional analysis of your system. In the OP case, the dimensional analysis ...
- 16.2k
11
votes
Accepted
NDSolve for Laplace equation on disk is not working
3 issues here.
You've mixed up polar coordinates and Cartesian coordinates. Since the equation is defined in polar coordinates, the shape of domain of definition is no longer a ...
- 63.8k
10
votes
Accepted
periodic boundary conditions and NDEigensystem
In the apparent absence of a direct solution using NDEigensystem to the periodic problem posed in the question, ...
- 60.8k
10
votes
Accepted
Inhomogeneous Neumann boundary conditions for diffusion equation
Updated Background
This is a more detailed response to a comment from the OP about the Neumann Value specification. The following is how I like to think of it.
I was initially confused on how to ...
- 16.2k
10
votes
Stokes equations in 2D with traction boundary conditions
As mentioned user21 for setting traction boundary conditions we need to know normal and tangent to the surface which is subjected to loading. On the inner surface ($r=a$) for the unit tangent vector ...
- 1,187
10
votes
Reciprocating flow in a channel over a heated surface
It seems that the main challenge in this problem is Dirichlet BC which should be switched periodically on $x=0$ and $x=L$. I don't know whether it possible to switch BC inside ...
- 1,187
9
votes
Accepted
DSolve, Partial equations, The arguments should be ordered consistently
DSolve is unable to solve this problem without assistance. Begin by solving the PDE only,
...
- 60.8k
9
votes
Accepted
Help with 3D FEM calculation of a heat equation
Solution in the case when the Neumann condition is given at all boundaries where possible
...
- 42k
9
votes
Accepted
Solve an ODE with parameters in a boundary condition
This question is particularly interesting to me, and I have a package that may be helpful to you here.
This particular equation is:
Fourth order
Linear
Inhomogeneous in the independent variable
...
- 5,613
9
votes
Accepted
Laplace equation with robin boundary conditions
Using DSolve
V 12.1 can solve this exactly.
...
- 137k
9
votes
Accepted
Numerically solve PDEs with constraints and without boundary solution
Linear PDEs typically are solved by the method of characteristics. For the PDE in the question, the ODEs of the characteristics are
...
- 60.8k
9
votes
Laplace's equation in spherical coordinates with Neumann b.c
In a previous answer 240190, I showed how one could use anisotropic meshing to add a DirichletCondition at "infinity" for a 1D problem. In this answer, I ...
- 16.2k
9
votes
Accepted
How can we apply specific boundary conditions with NDEigensystem?
"Different equations for different region" is not directly supported by NDSolve, NDEigensystem, etc. (at least for now)...
- 63.8k
8
votes
Accepted
Mathematica gets stuck trying to solve a simple differential equation
This does not get stuck, it returns right away
ClearAll[x,y]
z=1/1000;
DSolve[{1+x-x^2==D[2/(y[x]*(((1+ z x)/(2*y[x]))^2+1)),{x}],y[0]==0},y[x],x]
But your input ...
- 137k
8
votes
Accepted
Imposing boundary condition and normalization on an ODE
You can solve your problem by introducing a second ode (defining the antiderivative):
...
- 49.6k
8
votes
Accepted
Convergence of PDE solution using method of lines
There is a simple sign error in the set up I would think; the left NeumannValues needs a negative sign:
...
- 39.1k
8
votes
Accepted
Multiple Boundary Conditions for NDSolve in mesh with multiple interfaces
If I understand the question right, you could use boundary markers like so:
...
- 39.1k
8
votes
Balanced flux in FEA using NeumanValue
Too long for a comment. An easy way to generate a high quality mesh is to replace the Implicitegion with Cubuid and make use of ...
- 39.1k
8
votes
Laplace's equation in spherical coordinates with Neumann b.c
One can also consider the 3D statement of the problem. Solution of a such linear problem is not so time consuming nowadays. For mesh generation let's take advantage of ...
- 1,187
8
votes
Accepted
Integrating a ParametricNDSolve solution whose initial conditions are determined by another ParametricNDSolve function?
The problem can be solved using ParametricNDSolve twice, but a simpler approach is to use ParametricNDSolve once together with <...
- 60.8k
7
votes
Accepted
Solution of nonlinear system with boundary conditions
There is a solution satisfying all the boundary conditions for L = 2.665. I'll show you how to build this solution. First, we solve explicitly the first and third equations for the derivatives, we ...
- 42k
7
votes
Coupled elliptic pdes, FEM solver
Here is a partial solution; especially to the issues of @bbgodfrey 's answer. Let's look at the fourth-order ODE:
...
- 39.1k
7
votes
periodic boundary conditions and NDEigensystem
Version 11.0 has an additional boundary condition PeriodicBoundaryCondition. With this you can then use with NDEigensystem:
Here is an example with an unsymmetrical ...
- 39.1k
7
votes
Accepted
Eigenvalues of a fourth-order ODE
This problem can be solved symbolically, although perhaps not with DEigensystem. Instead, begin with DSolve.
...
- 60.8k
Only top scored, non community-wiki answers of a minimum length are eligible