Questions tagged [boundary-conditions]

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44 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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1answer
157 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...
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0answers
120 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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1answer
40 views

Problem with DSolve, NDSolve with WhenEvent, Boundary Value Problem

I got the same problem as in question: DSolve, NDSolve with WhenEvent Give Incorrect ...
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2answers
65 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)+\...
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45 views

Heat transport with Neumann bc in older Mathematica versions [duplicate]

Im trying to solve a simple heat transfer equation: $\partial_t T-\beta \partial_{xx}T=0$ for a finite system $x\epsilon <0;L>$ along with initial/boundary conditions: 1) $T(x,t)=0$ for $t<...
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1answer
73 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 ...
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1answer
101 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 ...
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0answers
62 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 ...
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1answer
39 views

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

I have two equations in 3 variables a2, b1, b2: ...
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2answers
111 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'\...
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2answers
60 views

How to connect boundary points of graph

I have the following data; ...
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1answer
203 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 ...
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0answers
49 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
80 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
75 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
62 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: ...
3
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1answer
108 views

How to use only Neumann boundary conditions and a normalization constraint on a PDE

I'm trying to solve the stationary PDE c = {{5, 0}, {0, 5}}; alpha = {x - 50, y - 50}; pde = Div[-c.Grad[u[x, y], {x, y}] - alpha*u[x, y], {x, y}]; (following ...
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1answer
133 views

How to solve transient 3D heat equation with robin boundary conditions

Good afternoon! I'm trying to solve the following heat equation: with the following boundary conditions and initial value: Nut I'm getting error while solving it with NDSolve: ...
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1answer
73 views

Numerically solving a system of ODEs with parameters [closed]

I am working on solving a system of coupled ordinary differential equations with initial values given. When I searched about my requirements I got the similar answer here. But I got another condition ...
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1answer
62 views

How do I formulate a Dirichlet boundary condition for which the boundary depends on the other variable?

I am trying to solve the Poisson equation on a cylindrical grid. $$ \frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial f(r, \theta)}{\partial r} = n(r, \theta) $$ Analytically, there is ...
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1answer
91 views

Problems with Neumann (zero flux) boundary conditions

I have the following code: ...
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1answer
216 views

Thermal conduction (Annulus, 2D): Missing boundary conditions

The thermal conduction problem, described in polarcoordinates can be solved ...
3
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1answer
87 views

Unable to use ElementMarker in DirichletCondition with structured quad mesh

I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error: ...
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0answers
84 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: ...
4
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1answer
153 views

Wave equation: Understanding PeriodicBoundaryCondition

Inspired by the interesting question 202542 I try to solve the wave equation with coupled boundary conditions u[x,t==1 ]==u[x,t==x/2] I tried ...
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0answers
40 views

Setting custom boundary conditions in pdetoode [closed]

I am solving a mix of PDE and ODE for two functions c1(x,t) and c2(t). Several answer point to the use of the function pdetoode. I would like to use that function, but set the my own boundary ...
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1answer
226 views

How to solve PDE with periodic and anti-periodic b.c.?

I need to solve the PDE for a complex function $A(x,t)=A_r(x,t)+iA_i(x,t)$ ...
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0answers
89 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 ...
1
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1answer
75 views

Errors from NDSolve [closed]

I'm trying to solve a system of PDEs with periodic boundary conditions using NDSolve. This works if I don't specify an initial condition (but is uninteresting, ...
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1answer
30 views
2
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1answer
100 views

Variation of the biharmonic equation with Neumann conditions

I am currently writing a script to plot the solution of a variant of the biharmonic equation. In this case the equation I want to solve is ...
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1answer
63 views

Coupled PDEs: Wave and String Equations

I need to solve a system of mixed string and wave equations. Omitting some constants it looks like this: $$u_ {\text {yy}} (y, t) - u_ {\text {tt}} (y, t) = \varphi _{t}(x, y, t)$$ $$\nabla _{\{x,y\}}...
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1answer
86 views

Laplace equation for cylindrical rods

I have a system of four cylindrical rods with a certain radius, length, and separation. I have applied different voltages to the rods. I want to solve the Laplace equation, but I am unable to give ...
3
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1answer
76 views

How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
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0answers
59 views

Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]

I am solving the 1-d wave equation with the following initial conditions: ...
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0answers
76 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 ...
3
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1answer
126 views

Eigenvalue dependent boundary conditions- mathematica

I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent. Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary ...
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0answers
67 views

NDSolve boundary condition relating derivatives in different variables [duplicate]

I am trying to solve a wave equation (2nd order PDE) in z and t with absorbing boundary conditions, i.e. a boundary condition that relates the partial z and t derivatives. For this particular example,...
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1answer
110 views

Periodic boundary conditions with multiple variables

I am trying to numerically solve the following first order coupled differential equations numerically, where i is an integer (can be set to zero), ...
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0answers
81 views

Solving 2d non-linear PDE with singular sources numerically [closed]

I would like to hear some suggestions on how to numerically solve a 4d Poisson equation with two singular sources, which can be brought to the following form (thanks to symmetries) \begin{equation} \...
6
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1answer
273 views

Neumann boundary condition is not satisfied

I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero: ...
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0answers
85 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 ...
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1answer
143 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 ...
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1answer
91 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
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1answer
231 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 ...
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2answers
85 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) ...
3
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2answers
317 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 ...
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1answer
81 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{\...