Questions tagged [boundary-conditions]

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330 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. ...
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172 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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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}}^{...
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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: ...
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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43 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
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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. ...
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 $g(t)$ ...
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 ...
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 "...
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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 ...
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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 ...
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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 ...
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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 ...
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0answers
169 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 ...
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0answers
204 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}{\...
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0answers
107 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 ...
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36 views

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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0answers
108 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 $f_{1}$, $f_{2}$, $f_{3}$, $f_{4}$, ...
0
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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}{\...
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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 (...
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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 ...
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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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68 views

Finding the solution of a PDE doesn't work

I'd like to find the solution of an ODE of order 2 : ...
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0answers
64 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 ...
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0answers
57 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 ...
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0answers
127 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{\...
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0answers
114 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: ...
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0answers
110 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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266 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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85 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)}{\...
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177 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 ...
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39 views

Finding good boundary conditions NDSolveValue

I have the following differential equation to solve : ...