Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
155
questions
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Problems with boundary conditions
I am new to mathematica and I have doubts with my code, I probably have errors with the boundary conditions
If you could help me I would appreciate it very much
my code is the following
...
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1answer
45 views
Give NeumannValue a nonlinear function
I have the following simpler example of my actual problem which reproduces my question
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3
votes
1answer
132 views
Finding solution for larger intervals with shooting method
I am trying to solve numerically the following non linear differential equation:
$ y''(x)+\frac{3}{x}y'(x)=\frac{{\rm d}V(y)}{{\rm d}y},\qquad V(y)=\frac{1}{4}(y(x)^2-1)^2+\frac{a}{2}(y(x)-1),$
with ...
0
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1answer
64 views
Analytical solution for ODE with a power-law term?
I want to solve the following differential equation which is a very common growth law model in biology — a generalization of the logistic equation. In this case, the equation possesses a power-law ...
2
votes
2answers
73 views
Boundary condition dependence on NDSolve inconsistent
In attempting to solve a fourth order system I have encountered an issue with the way NDSolve uses boundary conditions. Consider the following three different attempts:
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1
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0answers
91 views
General:: Exp[-717.401] is too small to represent as a normalized machine number; precision may be lost
I am solving pde.
For the post processing below, there is solution given in output which is the solution from mathematica version 10.0.1.
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0answers
107 views
Solve coupled partial differential equations with absorbing BCs
I try to solve the following system of coupled equations with NDSolve but the results seem to be not correct. I attached my code in which five dependent variables $f_{1}$, $f_{2}$, $f_{3}$, $f_{4}$, ...
2
votes
0answers
138 views
Solving a Modified Biharmonic Equation on a Square
I am seeking to solve the differential equation
\begin{equation}
\left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
7
votes
3answers
566 views
Solving heat equation on a cylinder with insulated ends and convective boundary conditions
I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
1
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0answers
89 views
PDE with boundary condition (differential equation)
I am trying to find a solution to this boundary value problem
$$h_t= \frac{1}{2} \sigma^2 x^2 h_{xx} + r x h_x \quad s.t.\\
Ah(b,t)+Bh_x(b,t)=g(t),$$
where $A,B,\sigma,r,b$ are constants and $g(t)$ ...
4
votes
3answers
207 views
Geometrically nonlinear beam deflection
Edit only for those interested in large deflections of beams
I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
0
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2answers
82 views
Error when using NDSolveValue. Lists are not the same shape
Please, help me with the following issue.
I am solving the following system of the coupled PDEs
with the following boundary conditions
and initial conditions.
After performing the following ...
1
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0answers
57 views
NDsolve Boundary Condition is a Function of the Solution
I am trying to solve something like Fick's Law using NDSolve:
$$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$
Subject to a ...
3
votes
1answer
79 views
Shooting Method with extra Unknown Condition
I've been trying to solve a system of 3 coupled 2nd order ODEs, for a real variable $x$, $0\geq x\leq \infty$. The equations are the following:
\begin{align}
&x^{2}\,h''(x) - x\,h'(x) + x^{2}\,g^{...
0
votes
0answers
68 views
solving a 2D eigenvalue problem for a partial differential equation
I'm fairly new to Mathematica and I'm looking for a way to solve a partial differential equation subject to periodic boundary conditions. The form of the equation looks like this:
$\frac{\partial^2}{\...
0
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0answers
37 views
Using NIntegrate/Integrate as boundary condition inside NDSolve
I try to implement a population model with age structure in Mma12 using NDSolve to get a numerical solution for my PDE. However, one boundary condition involves an integral, which gives me problems (...
2
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0answers
60 views
DSolve[] and initial conditions
Take some simple function of 2 variables, e.g. f[x_,y_] := x+y and try to solve a PDE of it for the general solution:
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1
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1answer
76 views
Asymptotic boundary conditions for differential equation
I am trying to solve the following equation ($\ell\in \mathbb{N}$)
$$f''(x)+\left(1-\dfrac{\ell(\ell+1)}{x^2}+\frac{2}{x}\right)f(x)=0,$$
with these two asymptotic boundary conditions (b.c.) on the ...
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0answers
90 views
Analytical Solution to Laplace over Irregular Domain using DSolve
I would like to find an analytical solution to a Laplace equation over the following irregular domain using a mix of Dirichlet and Neumann boundary conditions. I've spent a lot of time trying to use ...
1
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1answer
86 views
Half-absorbing boundary conditions
I'm trying to solve the spherically symmetric wave equation
$$0 = (\partial_t^2 - \partial_r^2 + 1)\phi(t,r)\,,$$
where $\phi(t,0) = 0$. Without doing anything fancy, we can solve this equation "...
3
votes
1answer
141 views
Stiff System of ODEs: NDSolve Convergence Issues
I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem.
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2
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1answer
123 views
NDSolve Convergence Issue for Coupled Field Problems
I have tried to use NDSolve to solve a coupled field Eqs (see the attached Codes). The MMA solver seems to failed to converge to the requested accuracy or precision within 100 iterations
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4
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1answer
79 views
Periodic extrapolation out of the domain of the solution of a PDE in two directions
As a prototypic problem
...
5
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1answer
512 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
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2answers
144 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
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0answers
33 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 ...
8
votes
2answers
274 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
232 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
154 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
206 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
25 views
What boundary conditions is mathematica enforcing by default? [duplicate]
I'm solving the PDE (Fokker-Planck equation)
$$\frac{\partial p}{\partial L}(L, \eta)=\frac{1}{L_{\mathrm{loc}}} \frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \frac{\partial p}{\partial ...
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0answers
31 views
How to define more general boundary conditions for ConvolutionLayer?
In Mathematica 12, I only see the option to define "PaddingSize" for a ConvolutionLayer in order to get Dirichlet boundary ...
5
votes
1answer
211 views
Mathematica vs. MATLAB: why am I getting different results for PDE with non-constant boundary condition?
I am trying to solve the same PDE in Mathematica and MATLAB, $\nabla^2\phi=0$ where $\phi=f(x,y)$ It has a Dirichlet boundary condition on the left, a section of non-constant Neumann boundary ...
3
votes
2answers
171 views
PDE solving for two different regions?
I have searched and read all previous questions but cannot get my head around this. I am new to mathematica.
I have two regions in 2D where I want to solve PDE. Of the form:
...
0
votes
1answer
43 views
Full domain of Dirichlet boundary not displaying in 3DPlot
I have code to solve the 2D wave equation on a given region with an initial condition that is sinusoidal in one part of the region and 0 elsewhere. Here is an example on a rectangular region that ...
2
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0answers
61 views
Modelling transparent boundary conditions on a quantum graph with Mathematica NDSolve and finite-element method
Continue to this issue
I am now trying to apply a solution from the question above to three-bonded star graph. My idea is to take the third bond at [10,20] because I am using only one function u[t,x]....
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0answers
64 views
3 dimensional Laplacian with 4 non-homogeneous boundary conditions
I have the 3-D Laplacian ($\nabla^2 T(x,y,z)=0$) defined over $x\in[0,L], y\in[0,l], z\in[0,w]$ with four non-homogeneous boundary conditions as follows:
$$T(0,y,z)=t_{hi}\tag1$$
$$T(x,0,z)=t_{ci}\...
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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
42 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
64 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
193 views
FEM: periodic solution of 2D Navier-Stokes equations
Let’s consider a horizontal channel with a round obstacle in the middle.
...
4
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1answer
286 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
$...
3
votes
1answer
125 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
74 views
Having error with solving BVP problem
I am trying to solve this differential equation but using my approach:
...
5
votes
1answer
95 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
199 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
116 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
254 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
272 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 ...
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0answers
68 views
