Questions tagged [boundary-conditions]

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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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1answer
45 views

Give NeumannValue a nonlinear function

I have the following simpler example of my actual problem which reproduces my question ...
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1answer
132 views

Finding solution for larger intervals with shooting method

I am trying to solve numerically the following non linear differential equation: $ y''(x)+\frac{3}{x}y'(x)=\frac{{\rm d}V(y)}{{\rm d}y},\qquad V(y)=\frac{1}{4}(y(x)^2-1)^2+\frac{a}{2}(y(x)-1),$ with ...
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1answer
64 views

Analytical solution for ODE with a power-law term?

I want to solve the following differential equation which is a very common growth law model in biology — a generalization of the logistic equation. In this case, the equation possesses a power-law ...
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2answers
73 views

Boundary condition dependence on NDSolve inconsistent

In attempting to solve a fourth order system I have encountered an issue with the way NDSolve uses boundary conditions. Consider the following three different attempts: ...
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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. ...
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107 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 $f_{1}$, $f_{2}$, $f_{3}$, $f_{4}$, ...
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0answers
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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3answers
566 views

Solving heat equation on a cylinder with insulated ends and convective boundary conditions

I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
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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 $g(t)$ ...
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3answers
207 views

Geometrically nonlinear beam deflection

Edit only for those interested in large deflections of beams I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
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2answers
82 views

Error when using NDSolveValue. Lists are not the same shape

Please, help me with the following issue. I am solving the following system of the coupled PDEs with the following boundary conditions and initial conditions. After performing the following ...
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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 ...
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1answer
79 views

Shooting Method with extra Unknown Condition

I've been trying to solve a system of 3 coupled 2nd order ODEs, for a real variable $x$, $0\geq x\leq \infty$. The equations are the following: \begin{align} &x^{2}\,h''(x) - x\,h'(x) + x^{2}\,g^{...
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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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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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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: ...
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1answer
76 views

Asymptotic boundary conditions for differential equation

I am trying to solve the following equation ($\ell\in \mathbb{N}$) $$f''(x)+\left(1-\dfrac{\ell(\ell+1)}{x^2}+\frac{2}{x}\right)f(x)=0,$$ with these two asymptotic boundary conditions (b.c.) on the ...
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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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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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1answer
141 views

Stiff System of ODEs: NDSolve Convergence Issues

I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem. ...
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1answer
123 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 ...
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1answer
79 views
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1answer
512 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 ...
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2answers
144 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 ...
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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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2answers
274 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 ...
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2answers
232 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. ...
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2answers
154 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 ...
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3answers
206 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 ...
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0answers
25 views

What boundary conditions is mathematica enforcing by default? [duplicate]

I'm solving the PDE (Fokker-Planck equation) $$\frac{\partial p}{\partial L}(L, \eta)=\frac{1}{L_{\mathrm{loc}}} \frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \frac{\partial p}{\partial ...
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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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1answer
211 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 ...
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2answers
171 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: ...
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1answer
43 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 ...
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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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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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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
42 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 ...
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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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1answer
193 views

FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
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1answer
286 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 $...
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1answer
125 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 ...
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1answer
74 views

Having error with solving BVP problem

I am trying to solve this differential equation but using my approach: ...
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1answer
95 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 ...
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2answers
199 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 ...
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1answer
116 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 ...
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3answers
254 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
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1answer
272 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 ...
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0answers
68 views

Finding the solution of a PDE doesn't work

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