Questions tagged [boundary-conditions]

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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 ...
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1answer
61 views

Errors from NDSolve

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, ...
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1answer
28 views
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1answer
42 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 ...
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1answer
52 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\}}...
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1answer
63 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 ...
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1answer
65 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. ...
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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: ...
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0answers
52 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 ...
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1answer
86 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,...
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1answer
81 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), ...
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0answers
66 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} \...
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1answer
174 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: ...
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0answers
70 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 ...
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1answer
102 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
56 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 ...
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1answer
179 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
82 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) ...
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2answers
238 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 ...
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1answer
67 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
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2answers
223 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
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1answer
52 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 ...
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1answer
103 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 ...
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1answer
104 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 ...
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2answers
177 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 $y(t,z)$ ...
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1answer
57 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 ...
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1answer
118 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^...
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4answers
491 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
28 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
83 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 ...
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0answers
92 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 ...
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1answer
154 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(...
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2answers
182 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(...
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0answers
24 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)\...
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1answer
92 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 $...
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1answer
193 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: ...
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0answers
134 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 ...
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0answers
42 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: ...
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1answer
204 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(\...
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1answer
101 views

How can I solve this BVP using mathematica?

I need to solve the following BVP: $$(g^{-1/3}f'')'+ff''=0$$ $$(g^{-1/3}g')'+0.71fg'=-1.43775g^{-1/3}(f'')^2$$ With the following constraints: $$f[0]=0,f'[0]=0,f'[20]=1,g[0]=0.944175,g[20]=1$$ I used ...
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2answers
120 views

Convergence of PDE solution using method of lines

I'm afraid that this will turn more into a math question rather than a Mathematica one. I'm trying to solve the equation $$\frac {\partial n}{\partial t}=D\frac {\partial^2n}{\partial x^2}$$ $$\...
3
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1answer
86 views

Problem involving a system of nonlinear coupled ODE's with adjustable boundary

The problem is to solve the following system ODEs: I. $\ \ \ \ \ \ \ \dfrac{4}{r}[1+a(r)]\left(\dfrac{dH}{dr}\right)^2+\dfrac{dG}{dr}=0$ II. $\ \ \ \ \dfrac{1}{r}\left(\dfrac{dA}{dr}\right)+f(r)+k^...
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1answer
165 views

Imposing boundary condition and normalization on an ODE

I want to use DSolve to solve a differential equation while imposing a boundary condition and normalization. How can I do that? Let's take for example a simple ...
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1answer
80 views

Boundary Condition Problem - Diffusion Equation

So, in my 1D diffusion equation, everything works as I would expect. ...
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1answer
69 views

Nonlinear differential equation system with initial conditions in the different point

I faced with unusual (at least for me) problems. I have a three nonlinear equations $ \dot x = f(x,y,z)\quad \dot y = g(x,y,z)\quad \dot z = h(x,y,z) $ and the following initial conditions $x(0)=1$,...
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0answers
51 views

Using NDSolve for coupled PDE's with moving boundary conditions [duplicate]

im trying to solve numerically a one dimensional case of "Stefan solidification problem". The equations, along with BC's and IC's are: I want to solve for P1(X,T),P2(X,T) and Xs(T) is the moving ...
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1answer
116 views

Find initial surface to minimize between two close curves

I have two close curves in space defined by $g$ and $h$ with: ...
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1answer
196 views

Solution of nonlinear system with boundary conditions

I'm try solve the following coupled ODEs with boundary conditions: $I. \ \ \ \ \ \ \ \dfrac{4}{r}[1+A(r)]\left(\dfrac{dH}{dr}\right)^2+\dfrac{dG}{dr}=0$ $II. \ \ \ \ \dfrac{1}{r}\left(\dfrac{dA}{dr}\...
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1answer
126 views

1-D heat equation with different thermal diffusivity at different regions

I am trying to solve this 1-D heat equation in the interval [-L1,L2] with the follow conditions:thermal diffusivity=alpha1 between [-L1,0);thermal diffusivity=alpha2 between (0,L2].Boundary conditions:...