Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
129
questions
4
votes
1answer
78 views
Periodic extrapolation out of the domain of the solution of a PDE in two directions
As a prototypic problem
...
5
votes
1answer
442 views
Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)
I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
2
votes
2answers
115 views
How to solve Nonlinear coupled ODEs using DSolve
I cannot solve such a system of coupled ODEs in MMA 12.1 using DSolve.
i.e. output is equal to the input equations ... (see the attached figure)
Here, each solution is labeled according to the name of ...
1
vote
0answers
29 views
How to specify the initial conditions with ParametricNDSolve
I am still working on this problem. I am trying to use shooting method since I do not know the correct value for the initial derivative. I am following this answer. Now the code looks like this (I ...
7
votes
2answers
252 views
Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)
I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
4
votes
2answers
213 views
Solving pde with boundary integral constraint
I want to solve a PDE, but I'm struggling a lot getting it into Mathematica.
This is what I currently have (thanks to @user21). However, there are still a couple of issues which I explain below.
...
2
votes
2answers
148 views
Specify a force on the entire body (e.g. gravity)
In the thread Stress calculations using finite elements User21 showed an example how to define a force over the entire body during FEM calculation as boundary condition. See the screenshot below from ...
6
votes
3answers
188 views
Balanced flux in FEA using NeumanValue
I'm using NeumannValue boundary conditions for a 3d FEA using NDSolveValue. In one area I have positive flux and in another area i have negative flux. In theory these should balance out (I set the ...
0
votes
0answers
23 views
What boundary conditions is mathematica enforcing by default? [duplicate]
I'm solving the PDE (Fokker-Planck equation)
$$\frac{\partial p}{\partial L}(L, \eta)=\frac{1}{L_{\mathrm{loc}}} \frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \frac{\partial p}{\partial ...
1
vote
0answers
25 views
How to define more general boundary conditions for ConvolutionLayer?
In Mathematica 12, I only see the option to define "PaddingSize" for a ConvolutionLayer in order to get Dirichlet boundary ...
5
votes
1answer
199 views
Mathematica vs. MATLAB: why am I getting different results for PDE with non-constant boundary condition?
I am trying to solve the same PDE in Mathematica and MATLAB, $\nabla^2\phi=0$ where $\phi=f(x,y)$ It has a Dirichlet boundary condition on the left, a section of non-constant Neumann boundary ...
3
votes
2answers
160 views
PDE solving for two different regions?
I have searched and read all previous questions but cannot get my head around this. I am new to mathematica.
I have two regions in 2D where I want to solve PDE. Of the form:
...
0
votes
1answer
40 views
Full domain of Dirichlet boundary not displaying in 3DPlot
I have code to solve the 2D wave equation on a given region with an initial condition that is sinusoidal in one part of the region and 0 elsewhere. Here is an example on a rectangular region that ...
2
votes
0answers
56 views
Modelling transparent boundary conditions on a quantum graph with Mathematica NDSolve and finite-element method
Continue to this issue
I am now trying to apply a solution from the question above to three-bonded star graph. My idea is to take the third bond at [10,20] because I am using only one function u[t,x]....
0
votes
0answers
64 views
3 dimensional Laplacian with 4 non-homogeneous boundary conditions
I have the 3-D Laplacian ($\nabla^2 T(x,y,z)=0$) defined over $x\in[0,L], y\in[0,l], z\in[0,w]$ with four non-homogeneous boundary conditions as follows:
$$T(0,y,z)=t_{hi}\tag1$$
$$T(x,0,z)=t_{ci}\...
1
vote
0answers
53 views
Integration resulting in imaginary result while solving a boundary value problem
I am trying to solve a boundary value problem involving a three-dimensional Laplacian $\nabla^2T(x,y,z)=0$ on the domain $x\in[0,L], y\in[0,l], z\in[0,w]$. I have six boundary conditions and based on ...
2
votes
0answers
36 views
Application of spatially varying boundary conditions and source term in AceFEM
I am trying to model a simple 2D steady state heat conduction problem using automatically generated Q2 elements.
The problem consists of a square domain with prescribed temperatures along the bottom ...
1
vote
0answers
56 views
Longitudinal Bar Vibration & Boundary Condition Problems
I am trying to solve the PDE for longitudinal vibrations in a bar (as shown for example at Youtube Longitudinal Bar Vibration). My challenge is the application I am trying to solve has these boundary ...
6
votes
1answer
181 views
FEM: periodic solution of 2D Navier-Stokes equations
Let’s consider a horizontal channel with a round obstacle in the middle.
...
4
votes
1answer
271 views
Approach to analytically solve a Coupled system of PDE in Mathematica [Heat transfer in cylindrical coordinates]
I have the following two PDEs, which describe steady-state coupled heat transport between a externally heated axi-symmetric solid body (Eq. 1, $T(r,z)$) and a fluid (Eq. 2, $t(z)$) flowing inside it
$...
2
votes
1answer
70 views
Numerically Solving a system of PDE (2 unknown functions)
I need to solve for function H[x,y] and V[x,y] on square {x,0,1},{y,0,1}, obeying the ...
2
votes
1answer
72 views
Having error with solving BVP problem
I am trying to solve this differential equation but using my approach:
...
5
votes
1answer
81 views
Assigning ElementMarkers to existing ElementMesh boundaries
I've imported a 2D element mesh from another program as a list of triangle coordinates {{x1,y1},{x2,y2}....} ("nodes") and element connections {{n1,n2,n3},...} ("elements"). Then I create an ...
7
votes
2answers
162 views
DEigensystem gives x-dependent eigenvalues
Bug introduced in Version 11 or earlier and persisting through 12.1. Reported to Wolfram Technical Support as CASE:4532301.
I am considering the eigenvalue problem associated with the double-well ...
4
votes
1answer
109 views
Trouble with dependent variables in NDSolve while modelling transparent boundary conditions on a quantum graph with Mathematica
I am trying to create a model of plane wave's propagation on a quantum graph(metric graph with a differential operator, Shrodinger operator in my case, along the edges and continuity condition at the ...
6
votes
3answers
225 views
How to define the boundary condition in 1D Heat transfer
I am trying to calculate the heat transfer among a 1-D rod, with one end insulated while the right end is immersed in constant temperature surface T=0. Assume that the initial temperature of the rod ...
6
votes
1answer
218 views
Laplace equation with robin boundary conditions
I want to solve the following steady state heat transfer problem with robin boundary condition at the bottom:
The following is the code for the transient solution, but how should I change the code ...
0
votes
0answers
66 views
3
votes
1answer
79 views
Plotting a differential equation with boundary conditions
I have a problem with numerical calculation and plotting of differential equation.
Now I set a complicated region to set a boundary condition:
...
0
votes
1answer
46 views
Analytically solve boundary-value problem with variables appearing inside integrand
I have an equation like this which I need to solve analytically. However, Mathematica seems to only accept f'[x] notation, which does not let me put any variables inside the derivative. See the ...
2
votes
1answer
115 views
Solving delay differential equation. DSolve returns `Indeterminate`
I want to solve the following systems of delay differential equations
$$
\text{SYSTEM 1}\\
x'(t) = -y'(t)-z'(t)\\
y'(t) = -z'(t) + x(t)y(t) \tanh(t)\\
z'(t) = -\Theta(t-2)x'(t-2)
$$
and
$$
\text{...
2
votes
1answer
168 views
Error in the solution of PDE with NDsolve and method of lines [closed]
I am trying to solve a system of the partial differential equation with the help of NDSolve and method of lines.
Mathematica code for the above-described problem is
...
2
votes
3answers
129 views
Specifying condition with NIntegrate
I have an integral
$$
P_{\frac12 + \mathrm i\mu}(\eta) = \frac{\sqrt{2}}{\pi} \cosh(\pi\mu) \int_{0}^{\infty} \frac{\cos(\mu\tau)}{\sqrt{\cosh\tau + \eta}} \mathrm d\tau, \quad \eta \geq 1, \quad \mu ...
0
votes
0answers
52 views
1D time-dependent Schrödinger equation with absorbing boundary
I'm trying to solve the 1D Schrödinger equation subjected to an absorbing condition using NDSolve but cannot seem to set up the absorbing condition...
My problem ...
2
votes
1answer
55 views
6
votes
1answer
253 views
Solve an ODE with parameters in a boundary condition
Consider the ODE:
ode = y''''[x] - 2*k^2*y''[x] + k^4*y[x] == I*k*a*((2*x - x^2 - c)*(y''[x] - k^2*y[x]) + 2*y[x]);
in which a...
1
vote
0answers
162 views
Coupled PDE equation or boundary condition creating singularity issue
Previous post: Using NDSolve and PieceWise for boundary conditions for coupled PDEs
I realised that my previous post was a little vague so I hope this post clarifies any confusion. I've looked over ...
0
votes
1answer
67 views
Problem with DSolve, NDSolve with WhenEvent, Boundary Value Problem
I got the same problem as in question:
DSolve, NDSolve with WhenEvent Give Incorrect ...
0
votes
2answers
69 views
Shooting with updating BC's
So I have a 'fairly simple' problem that needs to be 'solved'. I have been able to solve this running 2 loops in Matlab but I am sure Mathematica should be able to handle this. I have the ODE $$F'(x)+\...
0
votes
0answers
54 views
Heat transport with Neumann bc in older Mathematica versions [duplicate]
Im trying to solve a simple heat transfer equation: $\partial_t T-\beta \partial_{xx}T=0$ for a finite system $x\epsilon <0;L>$ along with initial/boundary conditions:
1) $T(x,t)=0$ for $t<...
1
vote
1answer
100 views
“Fewer dependent variables than equations, so the system is overdetermined” without any BC's
Consider this system of PDEs.
eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0
eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0
I would like to ...
3
votes
1answer
122 views
Solving Piecewise Differential Equation using NDSolve (coupling at BC)
I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
1
vote
0answers
62 views
BVP rooting method [duplicate]
How can I get the value of u'[-1], how can I know the StartingInitialConditions it used, why the output is just one solution
...
0
votes
1answer
52 views
How to solve an under determined system for a ratio of variables?
I have two equations in 3 variables a2, b1, b2:
...
5
votes
2answers
129 views
Eigenvalues of a fourth-order ODE
Consider the following ODE for $y(x)$ over $x\in\left[0,\frac{1}{2}\right]$ with an eigenvalue $\lambda$
$\qquad 2x\,y''''+ 4y'''=\lambda\, y''$
The boundary conditions at $x=\frac{1}{2}$ are $y'\...
0
votes
2answers
74 views
1
vote
1answer
212 views
Simplifying solution to a third-order Boundary Value problem
I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E.
The solution I get using this expression is really messy. Is there any way to simplify it ...
0
votes
0answers
55 views
Improving NDSolve robustness (not blowing up)
I am trying to solve a heat conduction equation in Mathematica 9. While I can get NDSolve to work in some conditions it appears to arbitrarily fail if parameters are modified even slightly. Eventually ...
0
votes
0answers
110 views
Solving time dependent boundary conditions heat PDE
I am attempting to solve the heat equation $\frac{\partial T}{\partial t}=\nabla^2T$, where $T=T(x,y,z,t)$, subject to the following boundary conditions:
$\frac{\partial T}{\partial x}|_{x=10}=\frac{\...
1
vote
0answers
150 views
Defining second derivative boundary condition using DEigensystem
I tried to solve a fourth-order eigenvalue problem with boundary conditions on high order derivative.
For example, the following equation,
$$\frac{\partial d}{\partial t}+\frac{\partial^4 d}{\...
