Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
200
questions
0
votes
0answers
53 views
Find correct boundary value to solve an ODE
This is the first time I am seeking help on this site. I am not sure whether the problem can be sovled. Actually, I am trying to solve an ODE
...
0
votes
0answers
50 views
Adding maximum value for function within diffusion equation
I have a function that I want to max out at a certain value, say 1 for simplicity. There is a pump that will heat in a certain area, but once its reaches the cap, it no longer heats past this (as if ...
0
votes
0answers
25 views
NDSolve with non local boundary condition
I'm interested in solving the 1D time-dependent Schrodinger equation $ i \partial_t u(x,t) = -\partial_x^2 u(x,t) + V(x,t) u(x,t) $ with a transparent boundary condition at, for instance, $x = x_0$ :
$...
2
votes
1answer
81 views
White plot and initial and boundary conditions
I am solving numerically the following hydrodynamics equations:
...
1
vote
0answers
44 views
How to set up a boundary condition on the diagonal of a region that restricts a partial derivative?
The problem is to solve the Laplace equation on a polygon with one of the boundary conditions specifying derivative on the boundary. Let us consider a polygon region.
...
0
votes
0answers
56 views
Error while using NDSolve
I'm trying to solve a PDE using NDSolve.
cfun = NDSolveValue[pde, c, {t, 0, tEnd},
DirichletCondition[c[t, x] == 5, x == 0], {x} \[Element] mesh];
I get the ...
0
votes
0answers
76 views
FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached
I have to solve a highly nonlinear parametric system of three PDEs.
I don't know to which extent the results are trustable. Indeed, the graph shown
by ParametricNDSolve also presents the error message ...
5
votes
2answers
117 views
Unable to solve nonlinear PDE with NDSolve
Lately, I've been trying to solve the following PDE:
\begin{equation} -v_0 |\nabla F| + {\bf f}\cdot \nabla F +D\nabla^2F = -1
\end{equation}
inside a 2D region between two disks both centered in the ...
0
votes
0answers
32 views
How to solve the problem with a particular “Boundary value condition”?
When I try to solve the boudary condition problem with the following code
...
1
vote
1answer
49 views
NDSolve second order diff eq with two boundary conditions?
I'm trying to reproduce some results from a paper. The problem is the following:
As you can see they say they can solve that equation with NDSolve. But there is no initial condition for y'. I tried:
<...
0
votes
2answers
110 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{...
7
votes
3answers
271 views
How to Solve Functional Differential Equation
I tried to solve this equation numerically.
eqnEx = x''[t] + x[2 t] == 0;
NDSolve[{eqnEx, x[1] == 10, x'[1] == 0}, x[t], {t, 1, 10}]
Two important character of the ...
9
votes
3answers
431 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:
...
1
vote
1answer
86 views
Modelling transparent boundary conditions on a three-bonded quantum graph
I've created two issue last year, but unfortunately was able to return to this problem only now.
This question is a continue to this issue.
Essentially I am now trying to apply a solution from the ...
0
votes
0answers
94 views
How to pose Dirichlet and Neumann BCs on same boundary?
Let' s look on the Laplace equation in a rectangle area:
Eq0 = Inactive[Laplacian][u[x, y], {x, y}]
\[CapitalOmega] = Rectangle[{0, 0}, {2, 1}]
and try to solve it ...
9
votes
1answer
396 views
Stokes equations in 2D with traction boundary conditions
This is a follow-up to a previous question (see here). We would like to solve the two-dimensional Stokes equations using the FEM package in Mathematica, when we prescribe traction boundary conditions. ...
1
vote
1answer
37 views
Making boundary condition a variable in ParametricNDSolve
I would like to make where my ODE is evaluated at (not the boundary condition itself but rather the "x" value of the boundary condition) to be a variable in my code. I find that Mathematica ...
0
votes
0answers
75 views
the question about second order differential equations
I have a second order differential equation with two known initial conditions like this:
...
4
votes
1answer
308 views
Stokes equations in 2D with Neumann conditions
I would like to solve the 2D Stokes equations within a unit disk, say $\Omega$, by using the finite element method (FEM) as it is implemented in NDSolve (by loading ...
0
votes
1answer
85 views
initial condition in finite element method
I want to apply the initial condition below to the linear element
c(x; 0) = sin(10πx); if x in [0; 0:1] and
c(x; 0) = 0; if x in [0:1; 1].
I tried like
...
4
votes
1answer
123 views
Mass Transfer Value
I'm trying to model the following boundary condition using MassTransferValue.
$$
D_A \frac{\partial[A]} {\partial x} + D_B \frac{\partial[B]} {\partial x}+ D_C \...
2
votes
1answer
65 views
Solving a Weak Interacting Gross-Pitaevskii equation with NDSolve
I am trying to solve the Gross-Pitaevskii equation for varying parameters, by creating a function:
...
1
vote
0answers
48 views
NDSolve with boundary conditions [closed]
I am trying to solve Laplace's equation with a boundary condition. The condition is that there is a box with zero potential on its walls, a 1D plate with potential V at the top of a two dimensional ...
0
votes
0answers
47 views
Conjugated Diffusion Equations
I am new to mathematical-biology and I have to solve the following (diffusion-like) equation
\begin{eqnarray}
\frac{\partial a(x,t)}{\partial t}= D \frac{\partial^2 a(x,t)}{\partial x^2}\\
\frac{\...
7
votes
2answers
564 views
Solving a 2D heat equation on a square with Dirichlet boundary conditions
I am trying to solve the following heat equation problem on the square [0,1]x[0,1].
\begin{equation*} \begin{gathered} u_t = u_{xx} + u_{yy} + f(x,y,t), \qquad u(x,y,0) = 0, \qquad u=0 \text{ on ...
5
votes
2answers
173 views
Is Shooting the best NDSolve method for two point conditions, and how to improve its accuracy?
Hi I have a two point conditions problem (controlled SIR epidemics via Pontryagin BVP), which is supposed to depend heavily on initial conditions, which break the problem into several cases (...
5
votes
2answers
202 views
Solving a heat equation on a finite interval with Neuman boundary conditions
I am new to Mathematica and need to verify my numerical result.
Can anyone please show me how to solve the following heat equation problem $$ u_t = u_{xx}$$
on the interval $ x \in [0,1]$. The initial ...
2
votes
1answer
74 views
NDSolve to automate shooting method (or others) for free boundary value problem?
I am trying to solve the following system of differential equations using NDSolve:
$$
\begin{align*}
f'(s) &= \frac{f(s)}{g(s)-s}\\
g'(s) &= \frac{g(s)}{f(s)-s}\\
f(0) &= 0\\
g(0) &= 0\...
4
votes
1answer
90 views
Solve numerically 2D parametric boundary problem
For a personal project, I want to solve the following problem:
Let $f\left(\boldsymbol{r}\right)$ be a 2D function, and let $\boldsymbol{r}\left(s\right)=\left(x\left(s\right),y\left(s\right)\right)$ ...
0
votes
0answers
64 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 ...
0
votes
1answer
88 views
Trying to find values of two parameters that match the boundary conditions defined
I have been trying to solve for the values of two parameters that satisfy the boundary conditions set for a set of equations set. The below is the code.
...
1
vote
1answer
62 views
DSolve a partial differential equation with two boundary conditions
While trying to solve:
$$
z \frac{\partial}{\partial z} (z G(s,z))=z \cosh (s) \frac{\partial}{\partial z} G(s,z)-\frac{1}{2}
\sinh (s) \frac{\partial}{\partial s} G(s,z)
$$
using DSolve it gives a ...
0
votes
0answers
59 views
Second-order nonlinear ordinary differential equation with some conditions
I just started to solve second-order nonlinear ordinary differential equation with boundaries condition I wanted to solve by DSolve but I know should be some ...
1
vote
0answers
69 views
DSolve for deflection of an elastic beam
I have to write a notebook about comparing the results of the deflection of an elastic beam, calculated with discrete methods and FE methods. The code has to be generalized for any kind of beam ...
4
votes
2answers
141 views
Numerically solve PDEs with constraints and without boundary solution
I have a PDE like
D[h[x1, x2], x1]*a[x1,x2]+D[h[x1,x2], x2]*b[x1,x2] + c[x1,x2] == h[x1,x2]
s.t. gradient(h(0,0))==0
where a,b,c are known functions of x1 and x2, ...
0
votes
1answer
52 views
How do I add a velocity boundary condition with specific time period
I have a wave equation for displacement and velocity, I want to add this boundary condition $v(x=0,\,t>0)=1$
My mathematica code is
...
1
vote
1answer
145 views
How can I solve a system of PDEs with constraints but having unknown boundary conditions
I have a 1st order system of two PDEs with two independent variables and two dependent variables.
...
2
votes
0answers
92 views
Trying to solve a PDE — getting warnings I don't understand
Consider the partial differential equation
...
0
votes
0answers
97 views
How to impose null divergence in the solution of NDEigensystem
I am trying to use NDEigensystem to find eigenvalues and eigenmodes of the following Laplacian with boundary conditions:
$$\vec{\nabla}^2 \vec{A}(x,z) = vals \; \...
2
votes
1answer
69 views
Trying to solve non-linear coupled differential equation with boundary conditions at different points
I'm trying to solve systems of dif. equations with boundaries conditions at distinct points such as:
...
2
votes
0answers
47 views
How to define smooth random initial conditions consistent with boundary conditions for this 1+2D PDE?
I wrote a fully working code to numerically solve a non-linear variation of the classic 1+2D waves equation. Here's a stripped down version of it (classic waves equation), with static initial ...
1
vote
1answer
109 views
Solving a system of PDE-ODE with Dirichlet condition
I'm trying to solve a system of one PDE and one ODE that are dependent on time and distance (H[x,t] and P[x,t]) with the distance varying between x = 0 and x = xmax. The value for function P is 0 at x ...
4
votes
3answers
328 views
Boundary value problem with a DiracDelta
It seems that Mathematica can solve an initial value problem with a DiracDelta, but not a boundary value problem with a ...
1
vote
1answer
136 views
Boundary conditions at infinity for 1+2D wave equation in Mathematica 7
To solve a waves equation, I need to define some boundary conditions. The wave is propagating on an infinite plane, and it's not a membrane fixed on some fixed support. I'm have difficulties in ...
2
votes
2answers
625 views
Three coupled PDEs to be solved semi-analytically/analytically
I have been trying to solve the following three coupled PDEs where the final objective is to find the distributions $\theta_h, \theta_c$ and $\theta_w$:
$x\in[0,1]$ and $y\in[0,1]$
$$\frac{\partial \...
0
votes
0answers
43 views
Problems with boundary conditions
I am new to mathematica and I have doubts with my code, I probably have errors with the boundary conditions
If you could help me I would appreciate it very much
my code is the following
...
0
votes
1answer
51 views
Give NeumannValue a nonlinear function
I have the following simpler example of my actual problem which reproduces my question
...
3
votes
1answer
143 views
Finding solution for larger intervals with shooting method
I am trying to solve numerically the following non linear differential equation:
$ y''(x)+\frac{3}{x}y'(x)=\frac{{\rm d}V(y)}{{\rm d}y},\qquad V(y)=\frac{1}{4}(y(x)^2-1)^2+\frac{a}{2}(y(x)-1),$
with ...
0
votes
1answer
83 views
Analytical solution for ODE with a power-law term?
I want to solve the following differential equation which is a very common growth law model in biology — a generalization of the logistic equation. In this case, the equation possesses a power-law ...
2
votes
2answers
74 views
Boundary condition dependence on NDSolve inconsistent
In attempting to solve a fourth order system I have encountered an issue with the way NDSolve uses boundary conditions. Consider the following three different attempts:
...
