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.
170
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3
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Solve Differential Equation Numerically
I investigated my system and encountered differential equation such as
$y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$,
where $d$ is a constant. The boundary condition is
$y'(0) = 30$
$y'(\infty)=0$.
I ...
- 33
2
votes
1
answer
139
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solving a system of partial differential equations
My naive code looks like the one in the picture
My problem is when I run it, I dont get any result. No error is thrown my way either. I just get a typesetted version of the NDSolve command. How do I ...
- 173
2
votes
2
answers
71
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Numerical solution of a nonlinear PDE that develops a growing piecewise linear region
I am trying to improve the numerical solution of some PDEs that develop a piecewise behavior during their evolution. The simplest example of one such PDE is for a function $u(t,x)$ with $t \in [-T,T]$ ...
- 163
1
vote
1
answer
65
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Plotting of graph after solving system of ODEs using NDSolve command
In the present question, I am trying to solve a system of ODEs with corresponding boundary conditions. After that, I tried to find Q, which is firstly dependent on z and then on M. Then, after using ...
- 87
0
votes
1
answer
71
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Non-minimal coupling ξ , Minkowski false vacuum decay case (shooting method) (An update to the previous question)
I asked a few days ago this question:
Non-minimal coupling ξ - numerical bounce solutions (shooting method, false vacuum decay)
Alex Trounev helped me improve my code building based on this paper (...
1
vote
1
answer
125
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Non-minimal coupling ξ - numerical bounce solutions (shooting method, false vacuum decay)
I have the potential below:
$$V(\phi)=-\frac14 a^2(3b-1)\phi^2+\frac12 a(b-1)\phi^3+\frac14 \phi^4 +a^4c$$
This potential has 2 minima, the false vacuum $\phi_f=0$ which tunnels to the global minimum, ...
9
votes
2
answers
309
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How do I pose Neumann boundary condition to suppress particles flux into zero point?
This is continuation from my previous post How to ensure for a solution of NDSolve to be positive? [https://mathematica.stackexchange.com/questions/278777/how-to-...
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7
votes
2
answers
283
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PDE involving derivative at boundary, with a boundary condition at infinity
I am trying to find the function $T(z,t)$ which solves this differential equation:
$$\frac{\partial T}{\partial t}=\frac{\partial^2 T}{\partial z^2}+St\left[ \exp\left [ -\frac{\left( x_f-Ut\right )^2}...
- 515
5
votes
1
answer
372
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False vacuum bounce solution (curved space) shooting method problems
Merry Christmas, I think I can still say it. I am back this time for my problem in a simpler case, without coupling. I have a problematic code now and I want your help. I want to solve numerically the ...
0
votes
1
answer
98
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Numerical solution of differential equation with DiracDelta fit boundary condition at zero poorly
I need to solve: $x^2y''(x)+(2x+1)y'(x)-x^2\omega^2y(x)=\frac{-\omega^2\delta(x-x_0)}{4\pi},x\in[0,\infty)$ with boundary conditions:$y(0)=1,\ y(\infty)=0$ , $\omega$ is a function of this form: ...
4
votes
2
answers
353
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Using Neumann boundary conditions for the wave equation
I have the following code to solve the wave equation in 2D:
...
4
votes
2
answers
221
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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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2
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490
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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
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0
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92
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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,
$$
for some function $\psi=\psi(\rho,z)...
4
votes
1
answer
210
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FEM derivative matrix construction
Assuming $A$ is a $3 \times 3$ matrix (and a function of $x$, and $z$) and $K_i, \beta_i$, and $\alpha(T)$ are known parameters, I need to solve the following equation, (with an implied sum over $\mu, ...
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5
votes
2
answers
711
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Numerical solutions of active 1D wave equations
I would like to solve the following PDE with finite difference method. The PDE is from the following paper, (https://arxiv.org/pdf/1911.11823.pdf). I would like to implement the algorithm for the left ...
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2
votes
0
answers
139
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Solving Delay PDE
I'm trying to numerically solve the following delay PDE:
$$
\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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0
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1
answer
107
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1
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3
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282
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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
649
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NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?
I am trying to used NDsolve to solve Nonlinear Schroedinger Equation:
...
- 711
2
votes
2
answers
290
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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:
...
- 121
1
vote
1
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162
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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?
...
- 121
0
votes
2
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241
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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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1
vote
2
answers
189
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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 ...
- 11
2
votes
0
answers
351
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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 ...
- 21
2
votes
3
answers
126
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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\...
- 21
2
votes
1
answer
368
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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
$$f^{\prime}(0)=0\qquad\lim_{z\to\...
1
vote
0
answers
181
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Laplacian and NDSolve and DSolve
I am trying to solve a simple test example using Laplacian. But I step from one problem to the next.
First I did not realized, that MMA uses spherical coordinates ...
- 45.4k
4
votes
1
answer
135
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Problem of step size effectively zero
I've been trying to solve the next system of differential equations which is very similar to this one in which I also sought help
Step size is effectively zero
$$F^2-G^2+HF'-F''+1=0$$
$$2GF+HG'-G''=0$$...
- 105
4
votes
2
answers
619
views
Dirichlet Condition at Infinity
I have the following system of diffusion equations with these boundary conditions.
The second condition is a Dirichlet condition at x approaching infinity. How do I implement that? I've tried ...
- 351
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0
answers
211
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Solving partial differential equation
I am new to mathematica and I want to solve the following pde. I have two boundary conditions and one initial condition.
I have tried the following code but the output is not the solution and it's ...
7
votes
3
answers
613
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Fourth-order BVP problem with boundary conditions at infinity
I am trying to compute the solution of the fourth-order ODE
$$ 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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6
votes
1
answer
745
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Step size is effectively zero
I've been trying to solve Bodewadt flow equations which is a system of differential equations.
$$\begin{align*}
F^2 - G^2 + HF' - F'' + 1 &= 0 \\
2GF + HG'-G'' &= 0 \\
2F + H' &= 0
\end{...
- 105
1
vote
1
answer
303
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Boundary conditions at infinity for 1+2D wave equation in Mathematica 7
To solve a waves equation, I need to define some boundary conditions. The wave is propagating on an infinite plane, and it's not a membrane fixed on some fixed support. I'm have difficulties in ...
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5
votes
1
answer
126
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Matching the solutions of diff. equations from forward and backward in some point
I am trying to solve two coupled non-linear differential equations for $F(r)$ and $h(r)$:
$$
\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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0
votes
1
answer
218
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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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5
votes
1
answer
534
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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 ...
- 53
3
votes
1
answer
186
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Coupled second order differential equation with NDSolve
I am trying to solve a 2nd order ODE to reproduce a plot.
Here are the equations:
...
0
votes
0
answers
169
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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 ...
0
votes
0
answers
99
views
0
votes
0
answers
57
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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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2
votes
1
answer
92
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Calculating the bounce solution numerically
I would like to obtain a numerical solution to the following example bounce equations,
$$\begin{align*}
\frac{\partial^2 a}{\partial t^2} &= \frac{1}{t^2} a(1-a)(1-3a)-\frac{b^2}{2}(1-a)\\
\frac{\...
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5
votes
1
answer
314
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Solve free boundary problem for heat equation
How can I use Mathematica to compute/approximate and plot the solution of the following problem?
$\min\{u_t - u_{xx} -1, u \} = 0 \text{ in } (0,T)\times (-1,1)$
$u(0,\cdot) = 0 \text{ in } (-1,1)$...
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4
votes
1
answer
169
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How to use NDSolve to solve 1+1 D heat equation $u_t=u_{xx}$ with $ -\infty<x<\infty$ and $0\leq t\leq T$?
How to use NDSolve to solve 1+1 D heat equation $u_t=u_{xx}$ with $ -\infty<x<\infty$ and $0\leq t\leq T$?
...
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0
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0
answers
82
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Finding the solution of a PDE doesn't work
I'd like to find the solution of an ODE of order 2 :
...
- 1,245
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0
answers
81
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Mathematica fails to solve diffusion pde(focker planck)
I am trying to solve the focker planck equation in mathematica. But this is showing lots of errors. i don't get where the problem lies.
The equation is
...
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2
votes
1
answer
197
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Error in the solution of PDE with NDsolve and method of lines [closed]
I am trying to solve a system of the partial differential equation with the help of NDSolve and method of lines.
Mathematica code for the above-described problem is
...
- 169
2
votes
0
answers
352
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Model 1D Vlasov Equation
Vlasov Equation
The non-relativistic form of the Vlasov equation is given by:
$$
\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
500
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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
226
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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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