# 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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### Fix boundary condition at infinity

I am working with this complicated PDE: ...
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### How to plot this BVP using shooting technique there is a problem in selecting the initial guess

I am trying to solve the flow and heat transfer problem. I am using the following code ...
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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 ...
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### 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 ...
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### Heat conduction problem with boundary at $\infty$

This is a 1-D heat conduction problem for a circular rod with 5cm, $T(x,0)=0$, $T(\infty, t)=0$, left boundary is insulated. I am trying to use the finite numerical method. My first question is how ...
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### 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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### 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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### Partial differential equation heat/diffusion equation 3d

I'm trying to solve the heat/diffusion equation in 3d in spherical symmetry $\partial_t f=D\Delta f$. I wrote : ...
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### How to solve a Bessel differential equation with a boundary condition at infinity?

I'm trying to solve a differential equation which solution is in the form of Bessel functions. One of the boundary conditions is at infinity. I use: ...
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### How to solve fourth order differential equation?

I have a differential equation of this type: y[x] - 1 - 2*l^2*y''[x] + l^4*y''''[x] == 0 (where l is a parameter and ...
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### How to solve this 2nd-order ODE with singularity?

I tried solving the eigenvalue problem of a 2nd-order ODE $$[b^2(k-2)^2y^2-2b(k-2)(1+2ky)+4k^2+b^2(k-2)3y]f(y) \\- 3b(3by-2)f'(y)\\-(3by-2)^2f''(y)=\lambda f(y)$$ with ...
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### Handling “ill-conditioned” system of ODE's with NDSolve

I am currently dealing with a system of coupled ODE's which I would like to solve numerically. I have already implemented the system in Mathematica using NDSolve. ...