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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.

2
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2answers
82 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
112 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 ...
7
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1answer
185 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
75 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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0answers
67 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
121 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
89 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
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1answer
49 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
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1answer
83 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 ...
3
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2answers
202 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
52 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
84 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
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1answer
88 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
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1answer
206 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
243 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
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2answers
186 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
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1answer
202 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
261 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
36 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
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0answers
77 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
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1answer
198 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
121 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 ...
1
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0answers
82 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 ...
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0answers
68 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
182 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
757 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
98 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
114 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
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1answer
264 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
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1answer
94 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) + \...
7
votes
2answers
216 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 $$r^2 a''(r)= a(r) [a(r)-1] [a(r)-2]- r^2 [1-a(r)] h(r)^2,$$...
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0answers
125 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 ...
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0answers
200 views

How to improve precision of finding the eigenfunction for this 2D Schrödinger equation?

I'm trying to solve a 2D Schrödinger equation with the following potential: ...
5
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1answer
271 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
274 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
291 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
264 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
355 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 ...
7
votes
0answers
237 views

How to use periodic boundary conditions on the derivative of u[x,y,z]?

I have a structural mechanical problem, where i try to calculate the strain field in the modelled material. I simplified the problem in the following example: There is a material with two phases, ...
2
votes
1answer
170 views

Errors when numerically solving differential equations for global vortex profiles

I am currently to numerically solve the following differential equation for the profile of global vortices with a simple complex scalar field: ...
3
votes
1answer
290 views

NDSolve with boundary condition at infinty

I have a nonlinear set of equations with a boundary condition at infinity. Consequently I have to shoot for the boundary. This question has some good ideas but there is an extra complication in my ...
3
votes
2answers
123 views

How to make an organised investigation of branch cuts from a solution to a differential equation

I am attempting to solve two differential equations. The solution gives equations that have branch cuts. I need to choose appropriate branch cuts for my boundary conditions. How do I find the correct ...
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0answers
75 views

PeriodicBoundaryConditions an a square

I hope the answer is simple, but I can't see the solution: I want to solve a PDE for u[x,y] under Periodic boundary conditions on say a square size 10 x 10. I.e. <...
2
votes
1answer
513 views

Solving the heat equation on the semi-infinite rod

Cross posted in scicomp.SE. I want to test the solution which is given below is right by Mathematica. Please look the post in mathstackexhange or Please look below. Question: Solve the ...
8
votes
4answers
647 views

Setting Up Boundary Conditions for Magnetostatic PDE

Bug introduced in 11.2.0 and fixed in 11.3.0 The system is a hollow cylinder (thin solenoid) with a current density $\text{J}$ and I'm looking to solve the magnetic potential ($\text{A}$) inside the ...
1
vote
1answer
206 views

How to solve this nonlinear differential equation?

The given nonlinear differential equation is y'''[t]+(y[t]*y''[t])+y[t]'^2-1=0 with boundary conditions {y[0]=0,y'[0]=0 and <...
1
vote
0answers
199 views

solving a nonlinear PDE of infinite cylindrical domain with NDSolve

I'm trying to solve the following nonlinear PDE Note that when n is equal to unit, the equation becomes linear. Thus, I applied the NDSolve function to solve it numerically. Here is my code: ...
2
votes
1answer
103 views

unknown cause of scaling factors in NDSolve solutions to a partial differential equation

I am trying to solve a coupled diffusion partial differential equation with a Gaussian profile at t = 0. I would like to see how the two functions, y and z, evolve in time and in one dimension. This ...
0
votes
0answers
69 views

Mathematica won't give any answer to a PDE system

I've been trying to double check Transformer Design book's solution to a PDE. Mathematica, however, gives me no answer. In other words, it just writes the DSolve expression back. Here is the equation: ...