Questions tagged [boundary-conditions]

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1answer
64 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
97 views

ParametricPlot inside of ParametricPlot

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 ...
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0answers
105 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
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1answer
94 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
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1answer
43 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
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1answer
85 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, ...
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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
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1answer
257 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
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1answer
121 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
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1answer
71 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
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0answers
106 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 ...
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0answers
62 views
1
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1answer
59 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
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1answer
114 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. ...
1
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0answers
50 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), \...
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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
129 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
30 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
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1answer
88 views

White plot and initial and boundary conditions

I am solving numerically the following hydrodynamics equations: ...
1
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0answers
53 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. ...
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0answers
61 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
120 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
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2answers
130 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 ...
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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
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1answer
59 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
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2answers
136 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
296 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
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3answers
505 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
91 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 ...
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0answers
97 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
444 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
40 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
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0answers
78 views

the question about second order differential equations

I have a second order differential equation with two known initial conditions like this: ...
4
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1answer
331 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
91 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
124 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
74 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
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0answers
50 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 ...
7
votes
2answers
653 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
183 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
227 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
91 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
93 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
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0answers
78 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
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1answer
90 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
80 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
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0answers
63 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
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0answers
77 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
146 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
58 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 ...

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