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Questions tagged [boundary-conditions]

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6
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0answers
56 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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0answers
53 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
39 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
130 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
74 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) ...
2
votes
2answers
181 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
63 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
175 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
48 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
76 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
73 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
170 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
52 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
93 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
403 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
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0answers
20 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
75 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
63 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
141 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
164 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
23 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
79 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
141 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
119 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
37 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
141 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(\...
0
votes
1answer
91 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 ...
3
votes
2answers
102 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
votes
1answer
83 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^...
5
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1answer
144 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 ...
1
vote
1answer
73 views

Boundary Condition Problem - Diffusion Equation

So, in my 1D diffusion equation, everything works as I would expect. ...
0
votes
1answer
67 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 $x(0)=1$,...
2
votes
0answers
50 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 ...
0
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1answer
108 views

Find initial surface to minimize between two close curves

I have two close curves in space defined by $g$ and $h$ with: ...
1
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1answer
188 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}\...
0
votes
1answer
116 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:...
2
votes
2answers
97 views

Spaced time mixed partial differential equation

I am trying to reproduce solution of the following differential equation. I know its solution is I tried the following code. ...
0
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0answers
68 views

Numerically solving a 3-dimensional partial differential equation with third order spatial derivatives

I am trying to numerically solve (and eventually plot evolving through time) the following differential equation $\frac{\partial f(x,y,t)}{\partial t} = i C_{0}\left(\frac{\partial^{2}f(x,y,t)}{\...
0
votes
0answers
91 views

Error with NDSolve/NDSolveValue: Boundary conditions aren't working!

I'm trying to solve the heat conduction equation for a 2D Steady State problem using NDSolveValue but it doesn't work with the specifc boundary conditions I need. I have a thin plate with natural ...
2
votes
1answer
103 views

Boundary values in PDE using NDSolve - different outputs whether v.10.2 or 11.3

I'm trying to solve the following PDE $$\frac{\partial n(t,x)}{\partial t}=f(t,x)\frac{\partial^2n}{\partial x^2}+\frac{\partial n}{\partial x}\frac{\partial f}{\partial x}$$ with the boundary ...
0
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0answers
32 views

Finding good boundary conditions NDSolveValue

I have the following differential equation to solve : ...
0
votes
1answer
89 views

Why isn't Derivative equal to NeumannValue? [duplicate]

Can someone explain why, if I have u=u[x,t] then Derivative[1,0][u][0,t] == 0 doesn't give the same result as ...
0
votes
1answer
72 views

Specifying different Neumann boundary values on different parts of a boundary

In Mathematica PDE solvers (say by FEM), the specification of Neumann boundary conditions is by specifying NeumannValue[..] (see Mathematica documentation, and also ...
1
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0answers
99 views

Applying Dirichlet and Neumann Boundary Condition for DSolve and NDSolve not computing [closed]

I'm interesting in solving this problem where I have a Dirichlet boundary condition at $\ x=0, u(x)=1$ and a Neumann boundary condition where at $\ x=25, du/dx=0$ I was able to get it to work when ...
3
votes
1answer
193 views

What's wrong with initial conditions?

I want to solve the nonlinear PDE for the anisotropic fluid flow: $-\rho*\partial{v_i}/\partial{t} + (C_{ijkl}v_{k,l})_{,j}-p_{,j} = 0$ (The nonlinear term $-v_jv_{i,j}$ will be added later) Here ...
6
votes
0answers
94 views

Solving ODE with assumption that solution is bounded at boundaries?

For a HW problem, this ODE had boundary conditions given that are not the normal boundary conditions, instead the problem says that solution $u(t)$ is bounded at the left and right ends of the domain. ...
1
vote
1answer
88 views

Solving Non-homogeneous BVP

Trying to solve a BVP sols1 = Simplify[ DSolve[{y''[x] - s*y[x] == -F[x], y'[0] == 0, y'[1] == 0},y[x], {x, 0, 1}]] The solution given $\frac{\left(e^{2 \sqrt{s} ...
0
votes
1answer
104 views

“conditional” initial condition for pde

I'm trying to solve a set of coupled pde equations of functions C1[t,x], C2[t,x]. all works fine but I need to specify a conditional initial conditions of the form: ...
0
votes
0answers
118 views

An iterative algorithm to obtain appropriate numerical solutions for the bounce

I am looking to replicate an algorithm explained in the paper "Impact of new physics on the EW vacuum stability in a curved spacetime background" by E. Bentivegna, V. Branchina, F. Continoa and D. ...
1
vote
1answer
96 views

Solutions to differential equation with differentiation with respect to two variables

I am attempting to numerically solve the following differential equation that includes differentiation with respect to two variables with two separate boundary conditions. $y^{\prime\prime}(x) + \...