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Questions tagged [boundary-conditions]

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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
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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
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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
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1answer
67 views
5
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1answer
202 views

Thermal conduction (Annulus, 2D): Missing boundary conditions

The thermal conduction problem, described in polarcoordinates can be solved ...
3
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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: ...
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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
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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 ...
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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
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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
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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
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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
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1answer
29 views
2
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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 ...
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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. ...
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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
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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
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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
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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
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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
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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
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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
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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(\...