Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
232
questions
1
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1answer
58 views
Unbounded solution at boundaries with few combination of values in this BVP solution
I had asked a question here regarding solution to a BVP problem. bbgodfrey provided an excellent answer using the method of integrated least squares.
However, for a few specific set of values of ...
0
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1answer
54 views
1
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1answer
84 views
1
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0answers
61 views
Unable to implement boundary conditions for a spherical wave equation coupled to a Laplace equation
I am having trouble setting up in Mathematica v 12.1 the following
system of coupled pdes on $r\in[0,10]$
$$ \left(\partial_t^2 - \frac{1}{r^2}\partial_r r^2 \partial_r \right) \theta(t,r) = -(1+2\Phi(...
2
votes
0answers
80 views
NDSolve gives different result if I use NeumannValue to set initial condition
While trying to get familiar with the NeumannValue function I tried solving the wave equation on $r\in [0,2\pi]$ for $\theta(t,r)$
$$\partial^2_t \theta - \partial^2_r \theta =0, $$
with intial ...
0
votes
1answer
57 views
ODE solution for a simple case
I was trying to solve this but I can't not fix the problem :( please help me.
a,b,f and d positive vale.
...
1
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0answers
109 views
5
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0answers
88 views
Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces
I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
0
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3answers
119 views
2
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3answers
173 views
Eigenvalue problem with NDSolve
I am trying to solve the following system of linear ODEs. It is an eigenvalue problem.
...
4
votes
1answer
116 views
NDSolve Warning: an insufficient number of boundary conditions. However, all boundary conditions are defined
I am trying to solve the system of equations (momentum conservation, heat, and polymerization equations) in the Couette problem. There are two planes, the bottom is fixed, the top is moving with the ...
1
vote
1answer
155 views
Find right end-point satisfying an integral constraint
I am solving the following system of first-order ODEs with a variable right-end point l1num and boundary condition at that point ...
2
votes
1answer
100 views
Solving boundary value problem with coupled odes at interface
I am trying to get the eigenvalues of the following differential system
...
2
votes
1answer
119 views
exact solution for first-order nonlinear ordinary differential equation [closed]
I was trying to solve this non-linear first ODE
...
0
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0answers
30 views
Boundary conditions are not satisfied after application of an interpolating function
I have a little question about boundaries conditions.
I solved a differential equation and these are x-dependent functions. They are classified using two indices (i,j) like:
...
1
vote
1answer
84 views
7
votes
3answers
171 views
Integrating a ParametricNDSolve solution whose initial conditions are determined by another ParametricNDSolve function?
I am trying integrate a ParametricNDSolve output (System2) whose initial conditions vary according to another ParametricNDSolve function (System1). The code I have so far is as follows.
...
2
votes
1answer
121 views
Using DSolveValue to get Analytic Solution to the Helmholtz Equation
I am trying to get Mathematica to verify my analytic solution to the following problem:
$$ \Delta u + u = 0 \quad\quad\text{on }\ D=[-3,3]\times[-3,3] $$
$$ u(x,y) = \sin(\frac{\pi x}{6}) \quad\quad\...
2
votes
3answers
136 views
Normalizing singularities in NDSolve
I've tried to create the following example. Suppose that I have the differential equation:
$$
U''(x) = \frac{U'(x) - U(x)}{x},
$$
which I know 1 boundary condition and know that this function should ...
0
votes
1answer
71 views
DSolve and Plot [closed]
I was working on this equation to solve and plot it, but I'm little bit confuse?!
...
2
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2answers
109 views
ParametricPlot inside of ParametricPlot [closed]
I don't know why the following is not working!
The code has a function y[x] then I have g[t] then I want to plot ...
0
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0answers
112 views
How do i solve two coupled nonlinear PDEs through Mathematica?
these are two relativistic fluid governing equations,
∂_t (γe)+∂_x(γev)=0
γ∂_t(γv)+∂_x[(γv)^2/2]=-(C/(1+C))*∂_x[log(e)]
where γ=1/sqrt(1-v^2) is Lorentz factor, <...
-1
votes
1answer
95 views
A No-linear differential equation
I'm recently figuring out how to make this equation solved but Mathematica does not solve this??!!
DSolve[{ y'[t]== ((3 a)/2 (y[t] - b/(2 a))^2 + k ((3 a)/2 - 1) t^-2 - ((a f)/2 + (3 b^2)/(8 a)))/(t ...
0
votes
1answer
48 views
Integrate and InverseFunction
I solve an easy example to check that Mathematica can understand the difference between ArcTan and ArcTanh but as you see here I can't get Arctanh??!! Even I don't know why the inverse function is not ...
1
vote
1answer
121 views
The heat equation on the intervall [0,1] with Robin Boundary
I have the heat equation on the invervall $[0,1]$, therefore I define
heqn = D[u[x, t], t] == D[u[x, t], {x, 2}];
and I define my initial data which can be boring, ...
0
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0answers
85 views
Non linear first DE with lot of parts
I want to know how I can solve this equation in Mathematica I guess I missed something!!
DSolve[ {a (h[a])^2 h'[a] +(nh[a]/ a^2) + m(h[a])^3 - l (h[a])^2 - t == 0}, h, a]
h[a] is my function and n,m,l,...
5
votes
1answer
260 views
Why DSolve solution to this PDE does not match NDSolve solution?
I was answering different question How Can I Visualize a PDE Boundary Condition? and in the process, found that DSOlve solution to the laplace PDE does not agree ...
-2
votes
1answer
125 views
How Can I Visualize a PDE Boundary Condition? [closed]
I want to use Mathematica to visualize boundary/initial conditions for PDEs in 3-dimensional space. This was sparked by the initial comment in this question, which attempts to solve the PDE $$\...
1
vote
1answer
74 views
System of PDE with integration conditions interior of domain
I am trying to solve this system of pde numerically. I am unable to find any method in Mathematica that can handle this problem. The issue is having this integration condition in the domain. I tried ...
1
vote
0answers
110 views
Boundary Value of Function Disagrees with Neumann Boundary Heat Equation
I'm trying to solve a time-dependent 2D heat equation with a source, initial specified heat distribution and heat flux loss at the boundary which goes with the temperature difference. Thus far, I've ...
0
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0answers
62 views
Problem with plotting a graph using NDSolve to solve a second degree problem
Here is the code I have been trying to solve:
...
1
vote
1answer
63 views
Use multiple initial conditions in parametric plots
I am plotting a 3d parametric plot for the set of my odes. I can use a single set of initial conditions to obtain a plot. I want to plot multiple initial conditions of my variables in a single 3d box. ...
2
votes
1answer
122 views
Neuman boundary conditions for system of PDE in 2D
The system of equations for three variables: n(x,y,t), b(x,y,t) and a(x,y,t)
The rest of letters are coefficients. System is defined over a square region with the lower left corner at the origin.
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1
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0answers
54 views
NDSolveValue BVP that encounters infinity
Problem setup:
I'm trying to solve the following, quite hairy, first order BVP problem, with four unknown functions $\phi, \theta, p_\phi, p_\theta$, and boundary conditions at $\phi(0), \phi(1), \...
0
votes
0answers
64 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
...
1
vote
1answer
146 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
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0answers
32 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
90 views
White plot and initial and boundary conditions
I am solving numerically the following hydrodynamics equations:
...
1
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0answers
56 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
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0answers
62 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
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0answers
139 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
139 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
34 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
62 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
147 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
302 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 ...
10
votes
3answers
560 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
97 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
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0answers
100 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 ...
11
votes
1answer
461 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. ...
