Questions tagged [boundary-conditions]

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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 ...
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1answer
54 views

Assumtion on Solve and DSolve

How to fix this problem I can't get something from this!! ...
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1answer
84 views

Non- linear ODE

I was working on this equation but I can't get out something for this: ...
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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(...
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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 ...
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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. ...
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0answers
109 views

A Simple equation [closed]

I don't know why is not working?!! ...
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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 ...
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3answers
119 views
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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. ...
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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 ...
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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
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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
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1answer
119 views

exact solution for first-order nonlinear ordinary differential equation [closed]

I was trying to solve this non-linear first ODE ...
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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: ...
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1answer
84 views

Plot a function inside of another function [closed]

I want to plot y[x] vs. x[t]: ...
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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
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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\...
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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 ...
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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 ...
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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, <...
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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 ...
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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 ...
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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, ...
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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
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 ...
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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
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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 ...
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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 ...
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0answers
62 views
1
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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
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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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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), \...
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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
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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 ...
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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, $x = x_0$ : $...
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1answer
90 views

White plot and initial and boundary conditions

I am solving numerically the following hydrodynamics equations: ...
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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. ...
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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 ...
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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
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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 ...
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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 ...
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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: <...
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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{...
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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 ...
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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: ...
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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 ...
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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
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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. ...

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