Questions tagged [boundary-conditions]

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4 votes
1 answer
187 views

Applying Dirichlet and Neumann boundary conditions seem to ignore Neumann boundary conditions

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Cedric Martens's user avatar
2 votes
1 answer
105 views

NDSolve: how to solve "ndnum error"

I have a problem of finding the shape of a current. please see the details here NDSolve does not accept the boundary condition I wrote a code but it gives the "ndnum" error. I tested the ...
AWer's user avatar
  • 35
0 votes
0 answers
52 views

NDSolve does not accept the boundary condition

I am new at Mathematica and trying to solve a nonlinear PDE with the help of NDSolve. H, the height of the current is a function of x and t. Based on the context I know the current has a parabolic ...
AWer's user avatar
  • 35
3 votes
1 answer
87 views

Piecewise BVP not working on interval for NDSolve [duplicate]

My Mathematica skills aren't the best but this solution isn't making sense considering the boundary value I am supplying. The leftmost boundary condition, i.e. at $x=0$, $c[t,x]$ should be $1$ for $t\...
Kendall's user avatar
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0 votes
1 answer
111 views

Help in solving the following bvp

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Trueee's user avatar
  • 41
2 votes
0 answers
114 views

Cavity resonator modeling with Wolfram Mathematica

I am attempting to determine eigenfrequencies and the corresponding electric field distribution in a rectangular cavity resonator with perfectly conducting walls. In the simplest case of a rectangular ...
Ian's user avatar
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0 votes
0 answers
60 views

How to get the boundary points from ConcaveHullMesh in 3D?

I am trying to visualize the boundary points of a quadratic polynomial that has only real roots where I treat the coefficients as coordinate values. But I am having a problem visualizing them because ...
Teg Louis's user avatar
  • 585
2 votes
1 answer
72 views

How can I use a loop inside a boundary condition in NDSolveValue?

How can I use the variable i of a "do" loop inside a boundary condition in NDSolveValue, and plot the solution for ...
Marcos 's user avatar
1 vote
2 answers
57 views

Solving BVP using shooting method and plotting the result

I am not able to obtain any plot with the following code. ...
Trueee's user avatar
  • 41
2 votes
1 answer
65 views

Solving DE with shooting method

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Trueee's user avatar
  • 41
0 votes
1 answer
68 views

How to set up "mixed" boundary conditions for NDSolve for PDE? [closed]

I have the following PDE that I am able to solve using DirichletCondition with NDSolve as the following: ...
user79317's user avatar
  • 125
1 vote
2 answers
178 views

Unexpected result for Poisson problem on torus (using PeriodicBoundaryCondition)

I want to solve the Laplace problem $-\Delta u=f$ ("analyst's Laplacian") for a given $f$ and unknown $u$ on the torus $[0,2\pi]/\sim$, i.e. a rectangle with opposite sides identified. The ...
user505117's user avatar
0 votes
1 answer
154 views

Partial differential equation with conditions

I am trying to solve this PDE with Mathematica, and I have checked the syntax a lot, but still don't get a solution ...
TTT's user avatar
  • 57
2 votes
1 answer
128 views

NDSolve ignores my NeumannValue boundary conditions

I am trying to solve a simple linear differential equation for $f(x,y)$ on a square with area $L\times L =1$. I consider $(\partial_x^2 + \partial_y^2)f + \partial_x \partial_y f = 0$ with the ...
B. Brekke's user avatar
  • 123
2 votes
2 answers
177 views

Badly conditioned matrix for boundary ODE

I have a coupled boundary ODE with dependent variables $u=u(x)$ and $z=z(x)$, $$u'' - \frac{1}{z} \left( -3 + u'^2 (3 - c\; e^{-g u} z^4) - 6 u' z' \right) = 0\tag{1}$$ $$z'' + c\; e^{-g u} z^3 (-3 + ...
mathemania's user avatar
1 vote
1 answer
54 views

First order differential equation with two conditions

I want to produce all possible solutions for this equation: ...
Mathecis's user avatar
  • 153
2 votes
1 answer
214 views

Machine overflow when defining boundary conditions

Recently I have been trying to code Maxwell's equations over a closed surface and have been facing some trouble defining the boundary conditions for the magnetic field. The equation for the normal of ...
Jole Stock's user avatar
2 votes
1 answer
106 views

Solving Poisson PDE with NDSolve and incomplete BC specifications

When solving the following PDE with a missing BC on the fourth edge ($y=1$): ...
anderstood's user avatar
  • 14.3k
2 votes
2 answers
104 views

NDSolve of a non-linear ODE

I am trying to solve the following non-linear ODE numerically: ...
Zazu's user avatar
  • 23
1 vote
1 answer
102 views

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
0 votes
0 answers
143 views

Iteration show different values in solving a pde in mathematica

I have a pde given below: $u_{t}-u_{xx}+\frac{1}{4}u=0, $ with boundary conditions $u(0,t)=1,\ \ u(1,t)=\frac{1}{2}e^{\frac{-t}{4}}+e^{\frac{-1}{2}},$ where $0\leq x\leq 1$. If the initial iterate is $...
Junaid Ahmad's user avatar
2 votes
2 answers
286 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
49 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
235 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
  • 231
3 votes
2 answers
248 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
118 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
  • 231
1 vote
1 answer
89 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
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
2 votes
0 answers
62 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
118 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
102 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
  • 1
1 vote
1 answer
218 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
112 views

Problem with PDE boundary and initial conditions

I am trying to numerically solve the following PDE ...
SaMaSo's user avatar
  • 231
2 votes
1 answer
203 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
  • 1,000
1 vote
1 answer
55 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
  • 165
2 votes
1 answer
208 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
108 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
220 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
1 vote
1 answer
214 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
  • 63
1 vote
0 answers
232 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
  • 21
3 votes
1 answer
154 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
1 vote
2 answers
191 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
  • 21
3 votes
2 answers
213 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
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
2 votes
1 answer
140 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
50 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
141 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
155 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
82 views

How to solve boundary value problem?

Is it possible to solve a boundary value problem like this? ...
AAA's user avatar
  • 197

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