Questions tagged [boundary-conditions]

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R-K fourth order scheme for system of ODEs containing 32 differential equations

In the present code, I am trying to solve the system of differential equations using the R-K fourth-order scheme. I am trying to plot the function u and T, but it is showing some error in the boundary ...
Komal Goyal's user avatar
2 votes
2 answers
126 views

Spherical Heat Equation and Convection Boundary Conditions

I'm trying to solve transient heat conduction equation in spherical domain in Mathematica. I made the simplifying hypothesis that temperature varies only with time and radial coordinate. The code is: <...
Julio Araujo Dos Santos's user avatar
0 votes
0 answers
29 views

NDSolve diverges with Neumann boundary condition [duplicate]

I am solving Poisson-like PDE with the Finite Element Method in Wolfram Mathematica. Only the Neumann boundary condition is imposed on the boundary. Of course, the solution is not unique, most likely ...
Ashot Matevosyan's user avatar
0 votes
0 answers
42 views

Graph plotting using system of ODE with NDSolve command

In the present question, I am trying to solve a system of ODEs with corresponding boundary conditions. And then, trying to plot the velocity function, but it shows some errors. Can anyone please help ...
Komal Goyal's user avatar
3 votes
3 answers
198 views

Solving a one-dimensional free-boundary problem with a singular boundary condition

Addendum (orginial question below). Thank you for the responses! After thinking some more about this problem, and thanks to @bbgodfreys helpful comment, I realised that the problem as posted below is ...
Anthony's user avatar
  • 155
3 votes
2 answers
233 views

How to accelerate FindRoot?

Original: I am running the following code to find the root of F , T and MM, here is an example ...
Mikoto's user avatar
  • 45
1 vote
0 answers
79 views

On formulating a Neumann boundary condition

I am attempting to follow this tutorial in the documentation on using FEM to solve PDEs. I am having difficulty understanding how to formulate the Neumann boundary condition for my free-boundary ...
Anthony's user avatar
  • 155
1 vote
1 answer
86 views

Solving a Variable Number of Difference Equations with RSolve

I'm trying to solve a variable number of linear equations defined by $$ \begin{align} x_0 &= A+Bx_1 \\ x_i &= C+\frac{B}{2}(x_{i-1}+x_{i+1}), \hspace{.25cm} 1\leq i \leq n-1 \\ x_n &= C+...
Mike D's user avatar
  • 113
1 vote
1 answer
65 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
2 votes
0 answers
46 views

Can Mathematica's FEM solve coupled Dirichlet Boundary Conditions?

I am solving a coupled system of PDEs using Mathematica's FEM capabilities. Specifically, the Navier-Stokes equations with a no-flux stress-free boundary. To do this, I need to specify a Dirichlet ...
Eric Hester's user avatar
0 votes
1 answer
116 views

How to minimize numerical error in the code while solving the system of ODEs

I just want to ask in the graph of the code mentioned in the link, while plotting u from {-0.0001,y,0.0001}, the jump is coming because of the numerical error u1-u2. Can anyone please tell me, how to ...
Komal Goyal's user avatar
-3 votes
1 answer
98 views

differential wave equations [closed]

By seeking a solution of ∂u ∂t = c 2 ∂ 2u ∂x 2 in the form u(x,t) = X(x)T(t), obtain and solve ordinary differential equations satisfied by X(x) and T(t). Hence write down possible solutions for u(x,t)...
kay's user avatar
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1 vote
1 answer
213 views

Solving a system of ODE using shooting technique with NDSolve command

In this code, I am trying to solve a system of first-order ODE with corresponding boundary conditions. But it is showing some error which I am not able to rectify. Can anyone help me in rectifying the ...
Komal Goyal's user avatar
1 vote
1 answer
101 views

Problem with PDE boundary and initial conditions

I am trying to numerically solve the following PDE ...
SaMaSo's user avatar
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1 vote
1 answer
116 views

Implementing and testing boundary conditions in polar coordinates for convection-diffusion equation

I am modeling a system using the convection-diffusion equation on a 2D, radially symmetric space. I wanted to do some sanity checks to make sure I am coding it correctly. I set up a situation where I ...
BioPhysicist's user avatar
1 vote
1 answer
51 views

Get the value of boundary point

I used the $NMinimize$ instruction to calculate, but what I got was the dt value of the red circle. If I want to obtain the dt value of the green circle, how do I obtain it? The code for generating ...
chen chen's user avatar
  • 143
2 votes
1 answer
202 views

How to model partial wavefunction collapse when part of a wavefunction hits a barrier?

This code models a complex Gaussian wavefunction expanding from the origin, part of which hits a barrier at x=10, Abs[y]<15. The code shows the wavefunction reflecting off the barrier, which is ...
Michael B. Heaney's user avatar
1 vote
1 answer
93 views

How to deal with differential algebraic equation (DAE) in ParametricNDSolve?

I have the following system of 10 differential equations where the first two equations are algebraic for u[t] and srz[t]. We ...
Dibbo123's user avatar
4 votes
4 answers
201 views

Solving PDE with power series

I would like to solve the PDE $$\partial_{x}f(x,y) + f(x,y)^2 = g(x,y)$$ with $f(0,0)=0$ and $\partial_y f(0,0)=0$ using a power series ansatz, i.e. I have an explicit expression for $g(x,y)=\sin(x+y)\...
António Borges Santos's user avatar
0 votes
1 answer
163 views

Drift-diffusion ODEs with two boundary conditions

I am trying to solve drift-diffusion equatons (Poisson's equation, continuity equations for electrons and holes and Kirchhoff's equation) for a reversely biased diode in a stationary state (no time ...
lygeon's user avatar
  • 53
1 vote
0 answers
164 views

Solution to a 2D Schrödinger equation

I am trying to solve a 2D Schrödinger equation with a complicated non-separable potential $V(z,\rho)$, $$ \nabla^{2}\Psi(z,\rho) +2(E_{0}-V(z,\rho))\Psi(z,\rho),$$ where $E_{0}$is the energy, $\hbar=m=...
Rom1984's user avatar
  • 11
3 votes
1 answer
145 views

Invalid PeriodicBoundaryCondition for Navier Stokes problem using NDSolveValue

Background: I'm looking to have a 2D re-entrant channel of a geophysical flow that is forced by a wind stress at the surface ("taux"; below) and experiences planetary rotation ("cor&...
Chris's user avatar
  • 33
0 votes
2 answers
147 views

Setting up a PDE for a time-independent Schrödinger equation

I am trying to solve a 2d Schrödinger equation with a non-separable potential because I want to calculate the probability of reflection for different angles of incidence of a plane wave. Here I ...
Rom1984's user avatar
  • 11
3 votes
2 answers
192 views

Stefan problem with mixed bc

I am trying to solve through Mathematica the classical Stefan problem $$ \left\{ \begin{array}{lll} \dot{v}(x,t)=v_{xx}(x,t) & x\in(0,s(t))\\ \dot{s}(t)=-v_x(s(t),t) & x = s(t)\\ v(0,t) = 0 &...
Josè's user avatar
  • 31
0 votes
1 answer
71 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
2 votes
1 answer
137 views

NDSolve with parametric endpoint

I want to solve numerically a system of ODEs of the form: $$\ddot{y}+3\frac{\dot{b}}{b}\dot{y}=2Cy(y^2-1)$$ and $$\dot{b}^{2}=1-b^{2}+\frac{D}{2\sqrt{C}}b^{2}\left(\dot{y}^{2}-C(y^{2}-1)^{2}\right)$$ ...
George Fanaras's user avatar
0 votes
2 answers
47 views

Constraints in a set of equations

I am currently working on a system of equations that is subject to a determinant constraint. Specifically, I have a matrix $B$ with $\det(B) = 0$, and I aim to construct a linear combination of its ...
Jorge Castaño's user avatar
1 vote
1 answer
125 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
4 votes
1 answer
148 views

DSolve solution for 1st order PDE involving complex number does not match initial condition

Bug introduced in 11.3 or earlier, persisting through 13.2.1. [Mathematica 12.0.0.0, MacOS X x86 (64bit)] Trying to solve ...
AlephBeth's user avatar
  • 175
0 votes
0 answers
73 views

How to solve boundary value problem?

Is it possible to solve a boundary value problem like this? ...
AAA's user avatar
  • 197
2 votes
1 answer
129 views

How to specify derivative boundary conditions for the gradient to be normal to the boundary?

I'm currently modeling an electric field with 2 charges. To do so, I use NDSolveValue to solve a Laplacian with 2 Dirichlet conditions on the voltages of the ...
mikemykhaylov's user avatar
3 votes
1 answer
131 views

Shooting technique using NDSolve

Here I am attaching my code below. It took all the variable's values, but the graph window was empty. I am not able to recognize, where is the error exactly. Differential equations were also, checked ...
Komal Goyal's user avatar
1 vote
1 answer
95 views

Shooting technique [closed]

Here is my code, I am trying to plot the graph of the differential equation, But output graph is an empty window. can anyone please help in getting the graphs. This equation is a modified bessel ...
Komal Goyal's user avatar
0 votes
0 answers
18 views

Difference Equation with Upper Boundary Condition, Lower Terms Not correct

I am struggling to understand the solution Mathematica is providing for the following recurrence relation As I have written a[i] I expected the following behavior <...
abnowack's user avatar
  • 113
2 votes
1 answer
87 views

Findroot: Boundary value problem

I have an equation, ...
a019's user avatar
  • 811
2 votes
0 answers
99 views

Implementation of Neumann-like boundary condition

If we wish to solve an elliptic PDE, say $\nabla^2\phi=\text{given}$, on a domain $\Omega$ with Neumann boundary conditions, $\hat{\mathbf{n}}\cdot \nabla \phi\Big|_{\partial \Omega}=\text{given}$, ...
Daniel Castro's user avatar
1 vote
2 answers
91 views

Plotting the solution of an equation

I just wondering if I can plot this solution? FullSimplify[Integrate[1/Sqrt[-1 + f/3 x^2 + b/x], x] , Assumptions -> {x > 0, f > 0, b > 0}]
Ali Dari's user avatar
2 votes
1 answer
94 views

A Simple Integrate

I'm facing the integral ...
Ali Dari's user avatar
0 votes
1 answer
90 views

Solve an equation for different values

I was trying to solve this equation for different value of a constant (a) but the solution is not different for those values?!! b and m are positive values. ...
Felipe Dura's user avatar
2 votes
1 answer
160 views

Unstable boundary values using NDSolve?

I have an equation: w1[u_]=-(1/2) u^2 ea e0 Sin[2 a[z]] + K (a''[z]) with numerical values, ...
a019's user avatar
  • 811
9 votes
2 answers
362 views

How can we apply specific boundary conditions with NDEigensystem?

I'm solving an eigenvalue problem with special b.c. mentioned in the paper Edge states in gated bilayer-monolayer graphene ribbons and bilayer domain walls. (See Eq.(3)(6)(7) and the paragraph after (...
valar morghulis's user avatar
5 votes
1 answer
372 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
2 votes
2 answers
152 views

NDSolve Extrapolating boundary conditions for FiniteElements

I'm trying to solve a 1+1 (1d time + 1d space) partial differential diffusion equation. My NDSolve call look basically like this: ...
Bomel's user avatar
  • 21
3 votes
1 answer
217 views

Coiling of flexible ropes (nonlinear BVP of ODEs with 10 unknown functions and 2 parameters)

I want to solve this ODEs with NDSolve, but it fails. The $F$(F), $\gamma$ (γ) is the given ...
JiahaoLi's user avatar
1 vote
1 answer
177 views

Solving Laplace PDE in mathematica

I'm trying to get the general solution for the Laplace equation: $\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0$ on the domain $\mathbb{R_0}\times\mathbb{R^+}\backslash\{(0,...
c.leblanc's user avatar
  • 111
6 votes
1 answer
327 views

Numerical solution of a partial derivative problem

WARNING: a couple of days ago I posted a similar question, but due to the impossibility of DirichletCondition[] to handle "cross-coupling of dependent ...
πρόσεχε's user avatar
3 votes
4 answers
278 views

I want to plot the solution but

I want to plot this solution for the different value of d and x but it is an Elliptic function. ...
Felipe Dura's user avatar
2 votes
3 answers
205 views

First order Differential equation with boundary condition

I'm wondering why it is not solving with the Mathematica?? ...
Felipe Dura's user avatar
2 votes
1 answer
155 views

Different answer using Dsolve or NDSolve to solve a PDE

I'm working on getting a numerical solution for the following PDE: $$ u_t-u_{xx}=0,\ x\in[0,1], t\in[0,1],\\ u(x,0)=\sin(2\pi x),\\ u(0,t)=0,\\ u_x(1,t)=2\pi e^{-t}. $$ The hand solution for this PDE ...
Charmbracelet's user avatar
2 votes
0 answers
78 views

Coupled PDEs with different dimensions and boundary conditions

The geometry of the problem is described by a cylinder inside a rectangular domain. The equations describes the region in between them. I have 2 PDEs for U(x,y,z) in the bulk region and V(z) for -0.5&...
Rz_PU's user avatar
  • 73

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