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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.

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Dealing with stiff differential equations in NDSolve

I have a problem with solving the following system of differential equations : $$\frac {d^2 f (x)} {dx^2} + \frac {1} {x}\frac {df (x)} {dx} = \frac {f (x)} {x^2} + f^3 (x) + f (x) g^2 (x) - f (x)...
ZaraReinm.'s user avatar
2 votes
1 answer
103 views

Solving two coupled 2nd order differential equations with 5 boundary values [closed]

Suppose I have two 2nd order differential equations: X''[r]+2X'[r]/r = 2(V[r]-u)X[r] V''[r]+2V'[r]/r = X[r]^2 with boundary values ...
Pratick Sarkar's user avatar
5 votes
1 answer
340 views

Solving third order DE from fluid dynamics

I am trying to use DSolve to solve a differential equation from G. Batchelor: An Introduction to Fluid Dynamics, eq. 5.12.4: [...] equation now reduces to $$\boxed{...
simon's user avatar
  • 47
2 votes
3 answers
202 views

Are there exact solutions for the following system of nonlinear first order ordinary differential equations?

The two equations are: u'[t]== -(K + L v[t]) u[t] and v'[t] == -L u[t] v[t] where K and L are constants. At t=0, u(0)=a ...
TNEst's user avatar
  • 21
0 votes
0 answers
100 views

Numerical solution of integro-differential equation where the integral term contains a double integral

I have the following code: ...
Pablo Escobar's user avatar
0 votes
1 answer
70 views

How to make code for boundary value problem?

I am trying to make graphs given by using this code but I failed. Please correct this code. ...
riaz iram's user avatar
0 votes
1 answer
140 views

Unsolved system of Nonlinear equations (bvp)

I am trying to solve the following system of equations: $\frac{df}{dr }=\frac{a}{r }\sin{f}$ $-\frac{1}{r}\frac{da}{dr}={\cos{f}-A}$ $\frac{1}{r}\frac{d}{dr}(r\frac{dA}{dr})-\frac{1}{r}\frac{da}{dr }=...
Andrey's user avatar
  • 133
0 votes
1 answer
125 views

Exponential and logarithmic functions slow the higher iterations in Mathematica

I want to solve BVP given in the (39)-(40) by the method given below these equations. I have written this method in Mathematica as follows. However, for n=1 it print the solution quickly but for ...
Junaid Ahmad's user avatar
3 votes
1 answer
159 views

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 ...
이영규's user avatar
2 votes
1 answer
154 views

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 ...
jboy's user avatar
  • 183
2 votes
2 answers
86 views

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 $t \in [-T,T]$ ...
bbrink's user avatar
  • 163
1 vote
1 answer
66 views

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 ...
Komal Goyal's user avatar
0 votes
1 answer
76 views

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 (...
Jennifer Derleth's user avatar
1 vote
1 answer
150 views

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, ...
Jennifer Derleth's user avatar
9 votes
2 answers
350 views

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-...
Igor Kotelnikov's user avatar
7 votes
2 answers
385 views

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}...
umby's user avatar
  • 585
5 votes
1 answer
417 views

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 ...
Jennifer Derleth's user avatar
0 votes
1 answer
103 views

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: ...
Artem Toropin's user avatar
4 votes
2 answers
586 views

Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
AccidentalTaylorExpansion's user avatar
4 votes
2 answers
250 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 ...
bbrink's user avatar
  • 163
11 votes
2 answers
761 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 ...
Zonova's user avatar
  • 341
1 vote
0 answers
95 views

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)...
Conner Dailey's user avatar
4 votes
1 answer
238 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, ...
Izek H's user avatar
  • 41
5 votes
2 answers
776 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 ...
little star's user avatar
2 votes
0 answers
166 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, \...
Ted's user avatar
  • 121
0 votes
1 answer
123 views

InverseFunction of ArcTanh and Log [closed]

I solved an equation and one solution was this: ...
Mathecis's user avatar
  • 153
1 vote
3 answers
351 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 ...
New User's user avatar
3 votes
1 answer
865 views

NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?

I am trying to used NDsolve to solve Nonlinear Schroedinger Equation: ...
user62716's user avatar
  • 731
2 votes
2 answers
360 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: ...
Laithy's user avatar
  • 121
1 vote
1 answer
171 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? ...
Paranoid's user avatar
  • 121
0 votes
2 answers
285 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{...
Brad's user avatar
  • 135
1 vote
2 answers
196 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 ...
Vitya's user avatar
  • 11
4 votes
0 answers
535 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 ...
Lyn Rin's user avatar
  • 41
2 votes
3 answers
144 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\...
cork_twist's user avatar
2 votes
1 answer
425 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\...
HeitorGalacian's user avatar
1 vote
0 answers
205 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 ...
Daniel Huber's user avatar
  • 52.7k
4 votes
1 answer
148 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 $$F^2-G^2+HF'-F''+1=0$$ $$2GF+HG'-G''=0$$...
Sebastián Frades's user avatar
4 votes
2 answers
738 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 ...
Walser's user avatar
  • 351
0 votes
0 answers
284 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 ...
Nazanin Variji's user avatar
7 votes
3 answers
672 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{...
Smerdjakov's user avatar
6 votes
1 answer
976 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{...
Sebastián Frades's user avatar
1 vote
1 answer
344 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 ...
Cham's user avatar
  • 4,093
5 votes
1 answer
148 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}...
Julia's user avatar
  • 53
0 votes
1 answer
237 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 ...
mattiav27's user avatar
  • 6,747
5 votes
1 answer
650 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 ...
haozz's user avatar
  • 53
3 votes
1 answer
197 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: ...
Bruna Mendonça's user avatar
0 votes
0 answers
190 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 ...
Mark Cairnie's user avatar
0 votes
0 answers
106 views

Fix boundary condition at infinity

I am working with this complicated PDE: ...
mattiav27's user avatar
  • 6,747
0 votes
0 answers
58 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 ...
Sanna's user avatar
  • 1
2 votes
1 answer
106 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{\...
Al Waurora's user avatar