# Questions tagged [boundary-condition-at-infinity]

Tag for differential equations satisfying boundary conditions at infinity, or with open boundary conditions, or defined on an unbounded domain.

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### Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
137 views

### Numerically solving nonlinear PDE $u_t = G(u,u_y,u_{xy},u_{xx}u_{yy})$ with unbounded initial condition

I am trying to numerically solve some nonlinear partial differential equations similar to the example given below, for which I have been unable to obtain stable numerical solutions due to some ...
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### Methods of Numerically Finding Function Minimizing Functional

Say we have some functional like the following: $H = (\partial_yf(y))^2 -w(y) f(y)^2 +f(y)^4/2$. This is the functional for the Gross Pitaevskii equation. Lets say $w(y)$, the trapping potential in ...
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1 vote
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### Numerical solutions of active 1D wave equations

I would like to solve the following PDE with finite difference method. The PDE is from the following paper, (https://arxiv.org/pdf/1911.11823.pdf). I would like to implement the algorithm for the left ...
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117 views

1 vote
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### Laplacian and NDSolve and DSolve

I am trying to solve a simple test example using Laplacian. But I step from one problem to the next. First I did not realized, that MMA uses spherical coordinates ...
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### Problem of step size effectively zero

I've been trying to solve the next system of differential equations which is very similar to this one in which I also sought help Step size is effectively zero $$F^2-G^2+HF'-F''+1=0$$ $$2GF+HG'-G''=0$$...
370 views

### Dirichlet Condition at Infinity

I have the following system of diffusion equations with these boundary conditions. The second condition is a Dirichlet condition at x approaching infinity. How do I implement that? I've tried ...
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### Solving partial differential equation

I am new to mathematica and I want to solve the following pde. I have two boundary conditions and one initial condition. I have tried the following code but the output is not the solution and it's ...
462 views

1 vote
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### Boundary conditions at infinity for 1+2D wave equation in Mathematica 7

To solve a waves equation, I need to define some boundary conditions. The wave is propagating on an infinite plane, and it's not a membrane fixed on some fixed support. I'm have difficulties in ...
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### Solve free boundary problem for heat equation

How can I use Mathematica to compute/approximate and plot the solution of the following problem? $\min\{u_t - u_{xx} -1, u \} = 0 \text{ in } (0,T)\times (-1,1)$ $u(0,\cdot) = 0 \text{ in } (-1,1)$...
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### How to use NDSolve to solve 1+1 D heat equation $u_t=u_{xx}$ with $-\infty<x<\infty$ and $0\leq t\leq T$?

How to use NDSolve to solve 1+1 D heat equation $u_t=u_{xx}$ with $-\infty<x<\infty$ and $0\leq t\leq T$? ...
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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 : ...
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### Mathematica fails to solve diffusion pde(focker planck)

I am trying to solve the focker planck equation in mathematica. But this is showing lots of errors. i don't get where the problem lies. The equation is ...
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### 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 ...
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### 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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### Using NDSolve to obtain solution

I am trying to solve the following ordinary differential equation but not getting result. Please help. Thanks My code is ...
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### Solving a BVP using NDSolve with conditions at infinity

I am trying to solve My code is ...
186 views

### Asymptotes of parabolic cylinder differential equations with boundaries at infinity

For context, I'm studying the paper Coulomb blockade in superconducting quantum point contacts by Averin from 1998. Specifically, I am trying to find how he obtains equation 11 from equation 10, which ...
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### Help in advection-dispersion equation using NDSolveValue

i have the advection-dispersion equation: Dz = 0.0000738739; as = 2.21622*10^-6; Dz*D[u[z, t], z, z] - as*D[u[z, t], z] == D[u[z, t], t] The boundary and ...
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### 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 ...
90 views

### Solving a Laplacian with boundary conditions at infinity

I'm trying to solve a Laplacian given the following boundary conditions: \begin{align*} V(x,y,0) &= 0\\ V(x,y, z \to \infty) &= 0\\ V(x,y, z = \sqrt{a^2-x^2-y^2}) &= 0 \end{align*} ...
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