Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
76
questions
0
votes
1answer
70 views
How to solve transient 3D heat equation with robin boundary conditions
Good afternoon!
I'm trying to solve the following heat equation:
with the following boundary conditions and initial value:
Nut I'm getting error while solving it with NDSolve:
...
2
votes
1answer
61 views
Numerically solving a system of ODEs with parameters [on hold]
I am working on solving a system of coupled ordinary differential equations with initial values given. When I searched about my requirements I got the similar answer here. But I got another condition ...
1
vote
1answer
50 views
How do I formulate a Dirichlet boundary condition for which the boundary depends on the other variable?
I am trying to solve the Poisson equation on a cylindrical grid.
$$
\frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial f(r, \theta)}{\partial r} = n(r, \theta)
$$
Analytically, there is ...
2
votes
1answer
67 views
5
votes
1answer
202 views
Thermal conduction (Annulus, 2D): Missing boundary conditions
The thermal conduction problem, described in polarcoordinates can be solved
...
3
votes
1answer
67 views
Unable to use ElementMarker in DirichletCondition with structured quad mesh
I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error:
...
0
votes
0answers
67 views
1D transport equation with Neumann conditions
I'm trying to solve 2nd order differetntial equation of heat transfer-type in a finite system x<0,L>, in particular:
...
4
votes
1answer
139 views
Wave equation: Understanding PeriodicBoundaryCondition
Inspired by the interesting question 202542 I try to solve the wave equation with coupled boundary conditions
u[x,t==1 ]==u[x,t==x/2]
I tried
...
1
vote
0answers
37 views
Setting custom boundary conditions in pdetoode [closed]
I am solving a mix of PDE and ODE for two functions c1(x,t) and c2(t). Several answer point to the use of the function pdetoode.
I would like to use that function, but set the my own boundary ...
3
votes
1answer
191 views
How to solve PDE with periodic and anti-periodic b.c.?
I need to solve the PDE for a complex function $A(x,t)=A_r(x,t)+iA_i(x,t)$
...
1
vote
0answers
73 views
How to impose a “boundary” condition inside a computing domain?
I need to set a "boundary" condition not at the boundaries of the computing domain but inside the domain during solving an ODE with FDM. The problem is a boundary value problem, which has been ...
1
vote
1answer
73 views
Errors from NDSolve [closed]
I'm trying to solve a system of PDEs with periodic boundary conditions using NDSolve. This works if I don't specify an initial condition (but is uninteresting, ...
0
votes
1answer
29 views
How to put boundary condition for linear set of differential equation?
I have the following code.
...
2
votes
1answer
65 views
Variation of the biharmonic equation with Neumann conditions
I am currently writing a script to plot the solution of a variant of the biharmonic equation. In this case the equation I want to solve is
...
-1
votes
1answer
58 views
Coupled PDEs: Wave and String Equations
I need to solve a system of mixed string and wave equations. Omitting some constants it looks like this:
$$u_ {\text {yy}} (y, t) - u_ {\text {tt}} (y, t) = \varphi _{t}(x, y, t)$$
$$\nabla _{\{x,y\}}...
-1
votes
1answer
75 views
Laplace equation for cylindrical rods
I have a system of four cylindrical rods with a certain radius, length, and separation. I have applied different voltages to the rods. I want to solve the Laplace equation, but I am unable to give ...
3
votes
1answer
72 views
How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?
Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows.
...
1
vote
0answers
58 views
Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]
I am solving the 1-d wave equation with the following initial conditions:
...
0
votes
0answers
66 views
Solving numerically an initial value problem on an unbounded domain
I wish to solve the pde:
$$-\frac{1}{1-t}\partial_x^2\phi+t^4(1-t)\partial_t^2\phi-t^4\partial_t\phi=\mu^2 \phi,$$
with initial conditions $\phi(x,0)=\cos(\mu x)$ and $\dot{\phi}(x,0)=0$ for some time ...
2
votes
1answer
98 views
Eigenvalue dependent boundary conditions- mathematica
I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent.
Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary ...
0
votes
0answers
67 views
NDSolve boundary condition relating derivatives in different variables [duplicate]
I am trying to solve a wave equation (2nd order PDE) in z and t with absorbing boundary conditions, i.e. a boundary condition that relates the partial z and t derivatives. For this particular example,...
1
vote
1answer
93 views
Periodic boundary conditions with multiple variables
I am trying to numerically solve the following first order coupled differential equations numerically, where i is an integer (can be set to zero), ...
2
votes
0answers
75 views
Solving 2d non-linear PDE with singular sources numerically [closed]
I would like to hear some suggestions on how to numerically solve a 4d Poisson equation with two singular sources, which can be brought to the following form (thanks to symmetries)
\begin{equation}
\...
6
votes
1answer
236 views
Neumann boundary condition is not satisfied
I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero:
...
6
votes
0answers
80 views
Direction of NeumannValue on boundary
When solving partial differential equations NeumannValue is used to specify the flux across the boundary. For normal fluxes the detailed notes state
They appear on the boundary ∂Ω of the region Ω ...
1
vote
1answer
117 views
Absorbing/Derivative Boundary Conditions
I am attempting to solve a differential equation, however I am having issues implementing boundary conditions that reduce the impact of reflections/instabilities.
I've had a look at similar ...
0
votes
1answer
71 views
Attempting PDE with inequality in boundary condition
I am attempting to solve the equation below, which requires v[y,0]==0 for all y greater than 0. I have followed the /; approach ...
7
votes
1answer
206 views
Absorbing Boundary Condition for Complex/Coupled PDE
Context: This question is relevant to the physical problem of an excited leaky cavity. The boundary condition on the inside of the cavity is Dirichlet. The other end of the cavity is partially blocked ...
1
vote
2answers
83 views
Stuck on solving differential equation
I have tried to solve :
$$\begin{array}{l} A\frac{1}{r}\frac{d}{{dr}}\left(
{r\frac{{du}}{{dr}}} \right) = - B + N{k^2}\frac{{{I_0}\left( {kr}
\right)}}{{{I_0}\left( {ka} \right)}}\\ BC:\\ u(r) ...
3
votes
2answers
297 views
NDSolve error in 2-D heat equation
I'm trying to solve the following PDE by Mathematica in 2-D case in the unit disk using polar cordinates,
where $\Omega$ is a bounded domain of $\mathbb{R}^n$, $\Gamma =\partial \Omega$ is the ...
0
votes
1answer
68 views
Solving a Partio-Integral Differential equation
I had a system of three PDEs
$$\frac{\partial \theta_h}{\partial x}+\beta_h (\theta_h-\theta_w) = 0$$
$$\frac{\partial \theta_c}{\partial y} + \beta_c (\theta_c-\theta_w) = 0$$
$$
\lambda_h \frac{\...
2
votes
2answers
280 views
boundary conditions involving time derivative
Can we solve the following PDE by Mathematica,
where $\Omega$ is a bounded domain of $\mathbb{R}^n$, $\Gamma =\partial \Omega$ is the boundary of $\Omega$, $\partial_\nu$ is the normal derivative, ...
3
votes
1answer
55 views
Creating Voronoi Mesh Region Bounded by Convex Hull (Possible problem with DiscretizeGraphics)
I want to create a MeshRegion that is VoronoiMesh bounded by the associated ConvexHullMesh. I followed the procedure in the answer for this post, but the resulting MeshRegion is very wrong.
This is ...
2
votes
1answer
118 views
Heat Equation with Mathematica Neumann / Dirichlet Conditions
This is the question I am trying to solve
After fours hours of research and 61 attempts (just today) on how to do this, I'm asking for help.
I've been in hospital and am now trying to catch up on ...
4
votes
1answer
124 views
Multiple Boundary Conditions for NDSolve in mesh with multiple interfaces
Here is my problem: I want to solve a Laplacian equation in a 2D geometry with multiple interfaces, each interface presenting a different boundary condition.
As for an example, I am working on a ring ...
1
vote
2answers
183 views
A numerical boundary conditions paradox
For $(t,z)\in[0,1]\times[-1,0]$
zmin = -1; tmax = 1;
and some fields $w(t,z)$ and $y(t,z)$
...
0
votes
1answer
60 views
How to force Mathematica to evaluate a limit in the boundary conditions of a differential equation?
I'm experiencing troubles in obtaining the result of an ordinary differential equation with a boundary condition at infinity.
I write down
...
1
vote
1answer
147 views
NDSolve: method of lines: unexpected error: insufficient boundary conditions
As a test of my ability to master the Method of Lines I tried to NDSolve the PDE's system
$$\partial_t \varphi = \varpi\qquad\partial_t\varpi=\frac{1}{r}\partial^...
4
votes
4answers
622 views
Inhomogeneous Neumann boundary conditions for diffusion equation
I am new to Mathematica and I have a problem specifying Neumann boundary conditions in diffusion equation. The best result I managed to get is this.
...
0
votes
0answers
34 views
NDSolve: Method of Lines: same grids for spatial discretization: error: stiff system_zero step size
How can I modify bbgofrey's answer so as to use $n+1$ grid points for variable $y$? My code
...
2
votes
1answer
85 views
EDP exotic boundaries condtions
I'm trying to numerically solve Laplacian(V(x,y)) = 0 on a cross having Dirichelet conditions on two opposite borders (e.g. V(0,x)=-10 and V(5,y)=-10) and having dV(x,y)/dx = const . dV/dy for ...
0
votes
0answers
134 views
NDSolve:Method of Lines: Spatial Discretization: bother doing it explicitly or just implement as internal routine?
My question is whether one's code must always contain the actual description of spatial discretization written explicitly or whether the Method of Lines can be called as an internal routine. If so ...
1
vote
1answer
164 views
NDSolve:PDE system, initial-boundary value problem:warning:NDSolve::mconly: For the method NDSolve`IDA, only machine real code is available
I tried to NDSolve the PDE system
$$\partial_t w =x\cdot w\quad\quad\partial_z x=w$$
for
$$(t,z)\in[0,1]\times[0,\pi]$$
with boundary conditions
$$x(t,0)=w(t,0)=w(t,\pi)=0$$
and initial conditions
$$w(...
3
votes
2answers
206 views
NDSolve:Coupled PDE's, initial-boundary value problem: unreasonable “insufficient number of boundary conditions” error
I tried to NDSolve the PDE system:
$$\partial_t y = x\partial_z w \quad\quad \partial_t w = \partial_z y \quad \quad \partial_z x=w $$
for $$(t,z)\in[0,1]\times[-1,0]$$
with initial conditions
$$x(...
0
votes
0answers
25 views
NDSolve unexpectedly terms boundary conditions insufficient in initial-boundary value problem
NDSolve can easily handle the PDE system $$\partial_t y = \partial_z w \quad\quad \partial_t w = \partial_z y $$ along with initial-boundary conditions $$w(t,0)=w(t,-1)=0\quad\quad w(0,z)=-sin^2(z\pi)\...
1
vote
1answer
109 views
Second-order nonlinear boundary value problem
I am trying to follow this work, in which Eq. (11), the 2nd-order, nonlinear differential equation depends on a pair of parameters $ (\kappa, h) $. But now I only care about the case with a vanishing $...
5
votes
1answer
237 views
Help with 3D FEM calculation of a heat equation
I want to solve a heat transport problem in a long tube where 4 coolings rods are inserted. Fluid flows down axially, and there's radial heat conduction.
First, the shape is defined:
...
5
votes
0answers
146 views
NDSolve post-processing: Calculate the flow over a FEM-boundary
I'm trying to calculate the heat loss from buried pipes with NDSolve`FEM. For this I set Dirichlet conditions at the model top and bottom and temperature dependant Neumann conditions at the contact ...
0
votes
0answers
45 views
NDSolveValue seems to ignore a boundary condition
I am trying to solve a system of PDEs over a cilyndrical region. The text goes as follows:
...
0
votes
1answer
260 views
Numerical solution of differential equation with boundary condition at infinity
I have the following ODE for a function $F(x)$: $F''-\frac{1}{x}F'-aF=0$ with the following boundary conditions: $F(x\to0) = 1$, $F(x\to\infty)=0$. It can be solved analytically: $F = \sqrt{a}xK_1(\...
