Questions tagged [boundary-conditions]

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2
votes
1answer
149 views

NDSolve Convergence Issue for Coupled Field Problems

I have tried to use NDSolve to solve a coupled field Eqs (see the attached Codes). The MMA solver seems to failed to converge to the requested accuracy or precision within 100 iterations ...
4
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1answer
89 views
8
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2answers
2k views

Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)

I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
2
votes
2answers
219 views

How to solve Nonlinear coupled ODEs using DSolve

I cannot solve such a system of coupled ODEs in MMA 12.1 using DSolve. i.e. output is equal to the input equations ... (see the attached figure) Here, each solution is labeled according to the name of ...
1
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0answers
40 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 ...
8
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2answers
303 views

Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
4
votes
2answers
320 views

Solving pde with boundary integral constraint

I want to solve a PDE, but I'm struggling a lot getting it into Mathematica. This is what I currently have (thanks to @user21). However, there are still a couple of issues which I explain below. ...
2
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1answer
190 views

Specify a force on the entire body (e.g. gravity)

In the thread Stress calculations using finite elements User21 showed an example how to define a force over the entire body during FEM calculation as boundary condition. See the screenshot below from ...
6
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3answers
277 views

Balanced flux in FEA using NeumanValue

I'm using NeumannValue boundary conditions for a 3d FEA using NDSolveValue. In one area I have positive flux and in another area i have negative flux. In theory these should balance out (I set the ...
1
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0answers
46 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 ...
6
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1answer
366 views

Mathematica vs. MATLAB: why am I getting different results for PDE with non-constant boundary condition?

I am trying to solve the same PDE in Mathematica and MATLAB, $\nabla^2\phi=0$ where $\phi=f(x,y)$ It has a Dirichlet boundary condition on the left, a section of non-constant Neumann boundary ...
3
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2answers
239 views

PDE solving for two different regions?

I have searched and read all previous questions but cannot get my head around this. I am new to mathematica. I have two regions in 2D where I want to solve PDE. Of the form: ...
0
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1answer
58 views

Full domain of Dirichlet boundary not displaying in 3DPlot

I have code to solve the 2D wave equation on a given region with an initial condition that is sinusoidal in one part of the region and 0 elsewhere. Here is an example on a rectangular region that ...
2
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0answers
78 views

Modelling transparent boundary conditions on a quantum graph with Mathematica NDSolve and finite-element method [duplicate]

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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0answers
69 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}\...
1
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0answers
57 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 ...
2
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1answer
102 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
94 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 ...
6
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1answer
290 views

FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
4
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1answer
371 views

Approach to analytically solve a Coupled system of PDE in Mathematica [Heat transfer in cylindrical coordinates]

I have the following two PDEs, which describe steady-state coupled heat transport between a externally heated axi-symmetric solid body (Eq. 1, $T(r,z)$) and a fluid (Eq. 2, $t(z)$) flowing inside it $...
3
votes
1answer
200 views

Numerically Solving a system of PDE (2 unknown functions)

I need to solve for function H[x,y] and V[x,y] on square {x,0,1},{y,0,1}, obeying the ...
2
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1answer
76 views

Having error with solving BVP problem

I am trying to solve this differential equation but using my approach: ...
5
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1answer
124 views

Assigning ElementMarkers to existing ElementMesh boundaries

I've imported a 2D element mesh from another program as a list of triangle coordinates {{x1,y1},{x2,y2}....} ("nodes") and element connections {{n1,n2,n3},...} ("elements"). Then I create an ...
8
votes
2answers
283 views

DEigensystem gives x-dependent eigenvalues

Bug introduced in Version 11 or earlier and persisting through 12.1. Reported to Wolfram Technical Support as CASE:4532301. I am considering the eigenvalue problem associated with the double-well ...
4
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1answer
141 views

Trouble with dependent variables in NDSolve while modelling transparent boundary conditions on a quantum graph with Mathematica

I am trying to create a model of plane wave's propagation on a quantum graph(metric graph with a differential operator, Shrodinger operator in my case, along the edges and continuity condition at the ...
6
votes
3answers
326 views

How to define the boundary condition in 1D Heat transfer

I am trying to calculate the heat transfer among a 1-D rod, with one end insulated while the right end is immersed in constant temperature surface T=0. Assume that the initial temperature of the rod ...
6
votes
1answer
528 views

Laplace equation with robin boundary conditions

I want to solve the following steady state heat transfer problem with robin boundary condition at the bottom: The following is the code for the transient solution, but how should I change the code ...
0
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0answers
76 views

Finding the solution of a PDE doesn't work

I'd like to find the solution of an ODE of order 2 : ...
3
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1answer
107 views

Plotting a differential equation with boundary conditions

I have a problem with numerical calculation and plotting of differential equation. Now I set a complicated region to set a boundary condition: ...
0
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1answer
51 views

Analytically solve boundary-value problem with variables appearing inside integrand

I have an equation like this which I need to solve analytically. However, Mathematica seems to only accept f'[x] notation, which does not let me put any variables inside the derivative. See the ...
3
votes
1answer
167 views

Solving delay differential equation. DSolve returns `Indeterminate`

I want to solve the following systems of delay differential equations $$ \text{SYSTEM 1}\\ x'(t) = -y'(t)-z'(t)\\ y'(t) = -z'(t) + x(t)y(t) \tanh(t)\\ z'(t) = -\Theta(t-2)x'(t-2) $$ and $$ \text{...
2
votes
1answer
182 views

Error in the solution of PDE with NDsolve and method of lines [closed]

I am trying to solve a system of the partial differential equation with the help of NDSolve and method of lines. Mathematica code for the above-described problem is ...
2
votes
3answers
206 views

Specifying condition with NIntegrate

I have an integral $$ P_{\frac12 + \mathrm i\mu}(\eta) = \frac{\sqrt{2}}{\pi} \cosh(\pi\mu) \int_{0}^{\infty} \frac{\cos(\mu\tau)}{\sqrt{\cosh\tau + \eta}} \mathrm d\tau, \quad \eta \geq 1, \quad \mu ...
0
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0answers
122 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 ...
2
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1answer
86 views

How to fix BC violation by NDSolve? Any typos?

The following piece of code ...
6
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1answer
373 views

Solve an ODE with parameters in a boundary condition

Consider the ODE: ode = y''''[x] - 2*k^2*y''[x] + k^4*y[x] == I*k*a*((2*x - x^2 - c)*(y''[x] - k^2*y[x]) + 2*y[x]); in which a...
1
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0answers
185 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 ...
0
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1answer
102 views

Problem with DSolve, NDSolve with WhenEvent, Boundary Value Problem

I got the same problem as in question: DSolve, NDSolve with WhenEvent Give Incorrect ...
0
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2answers
73 views

Shooting with updating BC's

So I have a 'fairly simple' problem that needs to be 'solved'. I have been able to solve this running 2 loops in Matlab but I am sure Mathematica should be able to handle this. I have the ODE $$F'(x)+\...
1
vote
1answer
303 views

"Fewer dependent variables than equations, so the system is overdetermined" without any BC's

Consider this system of PDEs. eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0 eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0 I would like to ...
3
votes
1answer
158 views

Solving Piecewise Differential Equation using NDSolve (coupling at BC)

I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
1
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0answers
68 views

BVP rooting method [duplicate]

How can I get the value of u'[-1], how can I know the StartingInitialConditions it used, why the output is just one solution ...
0
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1answer
151 views

How to solve an under determined system for a ratio of variables?

I have two equations in 3 variables a2, b1, b2: ...
5
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2answers
179 views

Eigenvalues of a fourth-order ODE

Consider the following ODE for $y(x)$ over $x\in\left[0,\frac{1}{2}\right]$ with an eigenvalue $\lambda$ $\qquad 2x\,y''''+ 4y'''=\lambda\, y''$ The boundary conditions at $x=\frac{1}{2}$ are $y'\...
0
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2answers
150 views

How to connect boundary points of graph

I have the following data; ...
1
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1answer
223 views

Simplifying solution to a third-order Boundary Value problem

I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E. The solution I get using this expression is really messy. Is there any way to simplify it ...
0
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0answers
63 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 ...
0
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0answers
201 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{\...
1
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0answers
407 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}{\...
5
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1answer
95 views

Why does this stiff BVP return unevaluated but a similar IVP produce a solution?

In Solving a steady-state viscous Burger's equation with NDSolve, one question involves the following problem: ...