# Questions tagged [boundary-conditions]

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### 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. ...
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 ...
138 views

### Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
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: ...
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]....
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 ...
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. ...
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 $g(t)$ ...
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 ...
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 "...
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 ...
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 ...
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 ...
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 ...
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 ...
204 views

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### Finding the solution of a PDE doesn't work

I'd like to find the solution of an ODE of order 2 : ...
64 views

### 1D time-dependent Schrödinger equation with absorbing boundary

I'm trying to solve the 1D SchrĆ¶dinger equation subjected to an absorbing condition using NDSolve but cannot seem to set up the absorbing condition... My problem ...
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 ...
127 views