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.
0
votes
0answers
49 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 ...
0
votes
0answers
81 views
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
...
0
votes
0answers
47 views
Solving nonlinear differential equation with boundary condition at infinity
I have a differential equation I am trying to solve using
DSolve[{f''[x] + f[x] - f[x]^3 == 0}, {f[x]}, x]
with the boundary condition $f(\pm\infty)\rightarrow \...
0
votes
1answer
126 views
2
votes
0answers
69 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 ...
2
votes
2answers
108 views
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 ...
1
vote
1answer
101 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 ...
0
votes
0answers
63 views
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 ...
0
votes
0answers
48 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*}
...
7
votes
1answer
177 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 ...
1
vote
1answer
76 views
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 :
...
3
votes
1answer
285 views
1st-order linear ODE system gives inaccurate/biased solutions
Consider an ODE eigensystem
$$
t(y+\frac{1}{s})a(y)+[(q+\frac{1}{2}+\frac{s}{2}y)+s(y\partial_y+\frac{1}{2})]b(y)=\lambda a(y)\\
t(y+\frac{1}{s})b(y)+[(q+\frac{1}{2}+\frac{s}{2}y)-s(y\partial_y+\frac{...
2
votes
1answer
115 views
How to solve this 2nd-order ODE with quadratic coefficients?
Consider an ODE eigensystem
$$
\begin{bmatrix}
0 & d_1-\mathrm id_2 \\
d_1+\mathrm id_2 & 0
\end{bmatrix}
\begin{bmatrix} a(y) \\ b(y) \end{bmatrix} = \lambda \begin{bmatrix} a(y) \\ b(...
2
votes
2answers
174 views
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:
...
1
vote
1answer
142 views
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 ...
9
votes
1answer
314 views
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 ...
1
vote
1answer
90 views
Second-order nonlinear boundary value problem
I am trying to follow this work, in which Eq. (11), the 2nd-order, nonlinear differential equation depends on a pair of parameters $ (\kappa, h) $. But now I only care about the case with a vanishing $...
0
votes
0answers
100 views
Solving ODE with NDSolve with initial condition at -Infinity
I have just started using Mathematica. I want to solve a differential equation numerically with NDSolve. I have to specify an "initial condition" at ...
3
votes
2answers
265 views
NDSolve with boundary conditions at infinity
I have a feeling that similar questions have been asked before, but here goes.
I'm trying to solve an ODE using NDSolve, with boundary conditions for one of the ...
0
votes
1answer
200 views
Numerical solution of differential equation with boundary condition at infinity
I have the following ODE for a function $F(x)$: $F''-\frac{1}{x}F'-aF=0$ with the following boundary conditions: $F(x\to0) = 1$, $F(x\to\infty)=0$. It can be solved analytically: $F = \sqrt{a}xK_1(\...
1
vote
1answer
66 views
Taking the limit of a parametric function produced by ParametricNDSolveValue
I'm working on a project for hard-sphere scattering, and to solve the for the phase function $\overline{\delta}_l(k,r)$ I use the variable phase equation
$$
\frac{d\overline{\delta}_l(r,k)}{dr} = -\...
0
votes
1answer
99 views
How can I solve this BVP using mathematica?
I need to solve the following BVP:
$$(g^{-1/3}f'')'+ff''=0$$
$$(g^{-1/3}g')'+0.71fg'=-1.43775g^{-1/3}(f'')^2$$
With the following constraints:
$$f[0]=0,f'[0]=0,f'[20]=1,g[0]=0.944175,g[20]=1$$
I used ...
4
votes
2answers
268 views
Why does NDSolve blow up when given my ODE but bvp4c in Matlab does not?
I am numerically solving the following ODE initially using NDSolve in Mathematica(updated and corrected):
$-(-\frac{z'(r)}{r \sqrt{z'(r)^2+1}}-\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}})=A_1(z(r)+H)...
1
vote
1answer
56 views
Mapping a boundary value problem: Jacobian in NDSolve and refining mesh close to a point
I would like to solve the (oversimplified!) BVP
$u''(x)-u(x)=0,\qquad x\in[0,\infty)$
with the condition $u(0)=1$. I thought to remap this into the BVP problem
$D[J^{-1}(\xi)u(\xi)]-J(\xi)u(\xi)=0, ...
2
votes
1answer
94 views
Specifying boundary conditions at $\infty$
I am trying to solve the coupled Ekman layer solutions numerically, but I am not sure how to enter the boundary conditions or begin to define the equations and write my code. These are my equations ...
1
vote
1answer
111 views
PDE in 3D: Specification boundary condition at infinity
I'm trying to solve the Schrodinger equation and having difficulties to define a
limitless region because the problem has the Dirichlet conditions at infinity. Maybe I don't need such a region and ...
7
votes
1answer
217 views
Instability, Courant Condition and Robustness about solving 2D+1 PDE
After several discussions, I would like to focus on the robustness of solving 2D+1 PDE by considering all suggested methods from @xzczd (see here)
I found that the Ratio between the convection term ...
2
votes
2answers
275 views
Solving 2D+1 PDE with Pseudospectral in one direction with periodic boundary condition?
According to the documentation about the pseudospectral difference-order:
It says:
Following the discussion here:
I found the messy behavior is always on the artificial boundary in $\omega$-...
3
votes
2answers
219 views
Nonlinear system of ODEs with boundary conditions
I'm trying solve this problem:
g'(r) = a(r)g(r)/r, (1/r)a'(r) = g(r)^2-1
which have the following boundary conditions: a(0)=n ...
1
vote
1answer
227 views
Solving Integro-differential equation numerically with shooting method
This question is related a question I previously asked here
Solving integro-differential equation with boundary condition at infinity
and for which a solution was found . Now I am dealing with a ...
3
votes
2answers
289 views
Solving integro-differential equation with boundary condition at infinity
I wish to solve a differential equation that contains a hard-to-evaluate integral and to plot the solution in a range at least $r\in(0,10)$. The equation comes from a Hartree equation (Schroedinger ...
0
votes
2answers
38 views
Force a result from “Indeterminate” for single impulse?
The formula for a single impulse of amplitude $1$ at $x=r$ is given by
$$\frac {\sin (\pi (x-r))}{\pi (x-r)}$$
(In MathJax because it's a math formula.)
Formally, at $x=r$, this function evaluates ...
2
votes
0answers
89 views
Initial condition trouble with NDSolve for a 2nd order PDE
In general, when solving a 2nd order PDE (such as the wave equation below) for $$u(x,t), \quad x \in(-\infty,\infty), \: t\in (0,\infty)$$ it should be sufficient to provide initial conditions $u(x,0)$...
5
votes
1answer
215 views
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. ...
3
votes
1answer
180 views
Boundary value problem for 2 coupled ODE's using NDSolve: “singularity or stiff system suspected”
I'm trying to solve a pair of coupled ODE's. I need to place four Dirichlet boundary conditions (at R = 0 and R = ∞ for each ...
2
votes
0answers
113 views
Boundary value problem, multiple dimensional shooting, coupled eigenvalue problem
Following the one dimensional boundary value problem here, I would like to understand the easiest way to solve a BVP for a coupled system. In the 1D case, BVP can be converted to an initial value ...
1
vote
0answers
97 views
How do I use NDSolve in Mathematica to solve a bvp by shooting method
I have the following sets of ordinary differential equations:
$f''=g\frac{g^2+\gamma^2}{g^2+\lambda \gamma^2}$
$g'=\frac{1}{3}f'^2-\frac{2}{3}ff''+Mnf'$
$(1+Rd)\theta''+\frac{2}{3}Prf\theta'+N_{b}\...
0
votes
2answers
202 views
NDSolve for a 4th order differential equation with boundary condition at Infinity [closed]
I would like to solve a 4th-order differential equation of the form:
$\partial^2_x\left(\,\frac{\partial^2_x\rho}{\rho}-\frac{1}{2}\left(\frac{\partial_x\rho}{\rho}\right)^2\right)= -2\lambda\rho$
...
13
votes
3answers
811 views
An ODE system easily polluted with spurious eigenvalues
I tried solving the eigenvalue problem of a 1st-order ODE system (see the code below)
with NDEigenvalue.
(One option I found in it seems to be ...
0
votes
1answer
110 views
“conditional” initial condition for pde
I'm trying to solve a set of coupled pde equations of functions C1[t,x], C2[t,x]. all works fine but I need to specify a conditional initial conditions of the form:
...
0
votes
0answers
123 views
An iterative algorithm to obtain appropriate numerical solutions for the bounce
I am looking to replicate an algorithm explained in the paper "Impact of new physics on the EW vacuum stability in a curved spacetime background" by E. Bentivegna, V. Branchina, F. Continoa and D. ...
0
votes
1answer
345 views
At t == …, step size is effectively zero; \ singularity or stiff system suspected
I need to get a phase portrait for a non-linear oscillator, for this I wrote down the corresponding equations. 3 equations for different "a" which can take values from minus to plus infinity. In each ...
1
vote
1answer
100 views
Solutions to differential equation with differentiation with respect to two variables
I am attempting to numerically solve the following differential equation that includes differentiation with respect to two variables with two separate boundary conditions.
$y^{\prime\prime}(x) + \...
8
votes
2answers
250 views
Error when solving 't Hooft-Polyakov radial equations using NDSolve
I'm trying to solve 2 coupled nonlinear ODEs using NDSolve, but the solution fails when the parameter $\lambda$ increases. The equations are
$$r^2 a''(r)= a(r) [a(r)-1] [a(r)-2]- r^2 [1-a(r)] h(r)^2,$$...
0
votes
0answers
133 views
Solving a differential equation modeling 2D convection
How can
$\qquad a_2\nabla^2 f(r,\theta) - \vec{g} \cdot \nabla f(r,\theta)= 0$
be solved for $f$? There is a symmetry in $\phi$ in spherical coordinates, so the equation is a 2D equation (depends ...
6
votes
1answer
378 views
NDSolve eigenvalue problem of bound state
I am trying to solve this eigenvalue problem:
\begin{align}
\mu \Psi(r) & =
-\frac{1}{2}\left ( \Psi^{\prime \prime}(r) + \frac{2}{r} \Psi' (r)\right )
-4\pi \Psi(r) \int _0^\infty dr' r'^2 \frac{...
4
votes
1answer
328 views
Variation of heat equation with guessed initial condition
Hi I am trying to solve a variation of the heat equation with interaction terms and external source -- actually it's the Schrödinger-Newton equation if that's more familiar to you.
\begin{align}
i \...
7
votes
2answers
357 views
Solve the heat equation for a semi infinite rod considering convection
Bug introduced in or after 10.3, persisting through 11.2.
I'm trying to solve following PDE (heat equation):
$$ \begin{cases} u_t = a \, u_{xx} \\ u(x,0) = 0\\ \lim_{x\to \infty}u(x,t) =0\\
\alpha\, ...
3
votes
2answers
292 views
Why ODE's naive finite difference matrix works well for different boundary conditions
We know finite difference method (FDM) can replace $y''(x)$ as $\frac{1}{h^2}[y(x+h)+y(x-h)-2y(x)]$ or so. The naive way to write down the matrix of the differential operator is like the following, ...
9
votes
1answer
394 views
${\frac {\partial^{2} u}{\partial {x}^{2}}} +{\frac {\partial ^{2} u}{\partial {y}^{2}}} =0$ with one boundary at infinity
Is there a trick to make Mathematica solve
$${\frac {\partial^{2} u}{\partial {x}^{2}}} +{\frac
{\partial ^{2} u}{\partial {y}^{2}}} =0$$ with one boundary condition at $\infty$?
Boundary ...
