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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52 views

Fix boundary condition at infinity

I am working with this complicated PDE: ...
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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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Calculating the bounce solution numerically

I would like to obtain a numerical solution to the following example bounce equations, $$\begin{align*} \frac{\partial^2 a}{\partial t^2} &= \frac{1}{t^2} a(1-a)(1-3a)-\frac{b^2}{2}(1-a)\\ \frac{\...
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1answer
92 views

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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1answer
67 views

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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66 views

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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60 views

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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1answer
169 views

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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136 views

Model 1D Vlasov Equation

Vlasov Equation The non-relativistic form of the Vlasov equation is given by: $$ \partial_{t} f\left( \mathbf{x}, \mathbf{v}, t \right) + \mathbf{v} \cdot \nabla f\left( \mathbf{x}, \mathbf{v}, t \...
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Boundary value problem using DTM-Pade

I have written the following code for solving a boundary value problem using DTM-Pade, but it is consuming a lot of time to execute. Can someone help me in rectifying the error in the code (if any) or ...
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419 views

Where is the numerical solving breaking down?

I am working with a set of three coupled reaction-diffusion PDEs, and for some parameter values I am getting some not so great solutions. I have been searching documentation and tutorials, and I have ...
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1answer
111 views

Solving 2D convection-conduction equation via using Fourier integral transform: the disappearance of the convection term?(with code)

I am currently solving a 2D convection-conduction equation. The convection is only working on the x direction. The governing equation and its associated conditions are given as where T is the ...
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169 views

How to solve this 1st-order linear ODE system with a few discrete eigenvalues?

I am trying to solve the eigensystem of a 1st-order linear ODE system in the region $(-\infty,\infty)$ and with Dirichlet boundary condition at the infinities $$ -i\partial_xu(x)+f^*(x)v(x)=\lambda u(...
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92 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 ...
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97 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 ...
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1answer
180 views
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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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135 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 ...
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1answer
202 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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92 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 ...
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64 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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1answer
261 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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1answer
340 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 : ...
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1answer
329 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{...
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1answer
140 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(...
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2answers
373 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: ...
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2answers
247 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 ...
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1answer
352 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 ...
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1answer
160 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 $...
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212 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 ...
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2answers
639 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 ...
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1answer
448 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(\...
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1answer
89 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} = -\...
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1answer
188 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 ...
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2answers
392 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)...
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1answer
62 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, ...
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1answer
114 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 ...
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1answer
191 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 ...
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1answer
255 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 ...
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2answers
363 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 $\omega$-...
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2answers
304 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 ...
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1answer
290 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 ...
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2answers
346 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 ...
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2answers
64 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 ...
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0answers
119 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 $u(x,0)$...
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1answer
260 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. ...
4
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1answer
286 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 ...
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0answers
177 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 ...