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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4 votes
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Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
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4 votes
2 answers
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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9 votes
2 answers
208 views

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
0 answers
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Selecting specific solutions from a differential equation using DSolve with difficult boundary conditions

Let's suppose I want to solve Laplace's equation in Axial Symmetry: $$ \nabla^2\psi=\partial^2_{\rho}\psi+\partial^2_{z}\psi+\frac{1}{\rho}\partial_{\rho}\psi=0, $$ for some function $\psi=\psi(\rho,z)...
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4 votes
1 answer
153 views

FEM derivative matrix construction

Assuming $A$ is a $3 \times 3$ matrix (and a function of $x$, and $z$) and $K_i, \beta_i$, and $\alpha(T)$ are known parameters, I need to solve the following equation, (with an implied sum over $\mu, ...
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5 votes
2 answers
588 views

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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2 votes
0 answers
117 views

Solving Delay PDE

I'm trying to numerically solve the following delay PDE: $$ \frac{\partial}{\partial t} f(x,t) = \int_{x+1}^\infty f(y, t) \hspace{0.2em} dy $$ given the initial conditions $$ f(x,0) = 0, \...
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  • 121
0 votes
1 answer
84 views

InverseFunction of ArcTanh and Log [closed]

I solved an equation and one solution was this: ...
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1 vote
3 answers
133 views

Analytical solution of second order linear differential equation with boundary at infinity

I am a new user to Mathematica and I would like to solve a simple second-order differential equation as follow: $y''[x]+\frac{(D-1)}{x}\times y'[x]=k\times y[x]$, where $D$ and $k$ are just two ...
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2 votes
1 answer
240 views

NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?

I am trying to used NDsolve to solve Nonlinear Schroedinger Equation: ...
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1 vote
1 answer
169 views

Solving an ODE with parameters and taking the limit of the solution

I am very new to Mathematica and already spent a lot of time trying to do this but failed. I am trying to solve an ODE: ...
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  • 111
1 vote
1 answer
136 views

How to solve this nonlinear boundary value problem?

I am new to Mathematica (or computations for that matter), can one please tell me how to solve these coupled differential equations, with boundary conditions on infinity, using NDsolve? ...
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0 votes
2 answers
161 views

DSolve to obtain a tanh solution

We are given a simple ODE with BCs: $\xi^2 \frac{df^2}{dx^2} + f - f^3 = 0$ $f(x=0) = 0$ $\\f(x\to\infty) = 1$ On paper this is quite easy to solve. One can obtain the solution $f(x) = \operatorname{...
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  • 135
1 vote
2 answers
172 views

I have some problems with NDSolve, my ODE is about Dynamics of Robot mechanism, and my BVP cannot be solved by NDSolve

Here are the parameters which are given in the task g = 9.81; h = 0.009; m1 = 4.5; m2 = 4.25; m3 = 3.3; L2 = 1.2; L3 = 0.8; \[Theta]CoM1 = 0.2; Matrixes of the ...
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10 votes
3 answers
681 views

Laplace's equation in spherical coordinates with Neumann b.c

I am trying to find the temperature field in a semi-infinite solid on whose surface there is an isotherm spherical cap sunken by a length p. For example: ...
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  • 425
2 votes
0 answers
201 views

BVPH Package 2.0

Hopefully you guys can help with this issue. I am currently using Mathematica package BVPH2.0 to solve hybrid nanofluid in boundary layer flow problem using homotopy analysis method. But I seem to ...
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2 votes
3 answers
110 views

ODE problem using DSolve

I would like to use DSolve (or NDSolve) to verify that the solution to the ODE problem -4(v''[t]+(2/t)v'[t])-2*v[t]*Log[v[t]]-(3+(3/2)Log[4 Pi])*v[t]==0, for $t\...
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1 vote
1 answer
169 views

Solving an ordinary differential equation with boundary condition at infinity

I want to solve the following differential equation f''[z] + (1/z)*f'[z] - f[z] + f[z]^3 == 0 subject to the boundary conditions $$f^{\prime}(0)=0\qquad\lim_{z\to\...
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1 vote
0 answers
134 views

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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4 votes
1 answer
118 views

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 $$F^2-G^2+HF'-F''+1=0$$ $$2GF+HG'-G''=0$$...
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4 votes
2 answers
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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  • 351
0 votes
0 answers
112 views

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 ...
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7 votes
3 answers
462 views

Fourth-order BVP problem with boundary conditions at infinity

I am trying to compute the solution of the fourth-order ODE $$ y^{\prime \prime} + V(y) - \beta y^{\text{ (IV)} } = 0$$ with $V(x) = -2x + 4 x^3$, on the real line, with boundary conditions $$ \begin{...
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5 votes
1 answer
333 views

Step size is effectively zero

I've been trying to solve Bodewadt flow equations which is a system of differential equations. $$\begin{align*} F^2 - G^2 + HF' - F'' + 1 &= 0 \\ 2GF + HG'-G'' &= 0 \\ 2F + H' &= 0 \end{...
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1 vote
1 answer
229 views

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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  • 3,533
5 votes
1 answer
100 views

Matching the solutions of diff. equations from forward and backward in some point

I am trying to solve two coupled non-linear differential equations for $F(r)$ and $h(r)$: $$ \begin{aligned} F''-F(F^2-1)/r^2- Fh^2&=0 \\ h''+2h'/r-2F^2h/r^2+\beta^2/2 h(1-h^2)&=0 \end{aligned}...
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  • 53
0 votes
1 answer
129 views

How do I enforce this boundary condition?

I am solving this differential equation: (1 - 2 M/r) D[(1 - (2 M)/r) D[q[r], r], r] - (1 - 2 M/r) ((l (l + 1))/r^2 - (6 M)/r^3) q[r] with the boundary conditions ...
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  • 6,134
5 votes
1 answer
293 views

Trouble with the shooting method for boundary value problem of a 4th-order ODE

This is a question about the fluid mechanics equation, which is solved by a similarity solution ($f(t)$, here). I'm trying to solve the following boundary value problem with shooting method (taken ...
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3 votes
1 answer
156 views

Coupled second order differential equation with NDSolve

I am trying to solve a 2nd order ODE to reproduce a plot. Here are the equations: ...
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0 votes
0 answers
132 views

Analytical Solution to Laplace over Irregular Domain using DSolve

I would like to find an analytical solution to a Laplace equation over the following irregular domain using a mix of Dirichlet and Neumann boundary conditions. I've spent a lot of time trying to use ...
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0 votes
0 answers
82 views

Fix boundary condition at infinity

I am working with this complicated PDE: ...
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  • 6,134
0 votes
0 answers
53 views

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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  • 1
2 votes
1 answer
76 views

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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5 votes
1 answer
236 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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  • 51
4 votes
1 answer
141 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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  • 281
0 votes
0 answers
77 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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  • 1,225
0 votes
0 answers
78 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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2 votes
1 answer
187 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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2 votes
0 answers
284 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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14 votes
4 answers
483 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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2 votes
1 answer
177 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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  • 329
8 votes
1 answer
229 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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  • 4,104
0 votes
0 answers
127 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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  • 367
0 votes
0 answers
103 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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0 votes
1 answer
291 views

Solving a BVP using NDSolve with conditions at infinity

I am trying to solve My code is ...
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2 votes
0 answers
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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  • 1,319
2 votes
2 answers
164 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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2 votes
1 answer
383 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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0 votes
0 answers
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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  • 111
7 votes
1 answer
385 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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  • 133