Questions tagged [boundary-conditions]

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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 ...
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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 ...
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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, $x = x_0$ : $...
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1answer
81 views

White plot and initial and boundary conditions

I am solving numerically the following hydrodynamics equations: ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: <...
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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{...
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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 ...
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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: ...
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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 ...
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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 ...
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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. ...
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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 ...
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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
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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 ...
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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 ...
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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 \...
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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: ...
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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 ...
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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{\...
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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 ...
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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 (...
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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
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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\...
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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 $\boldsymbol{r}\left(s\right)=\left(x\left(s\right),y\left(s\right)\right)$ ...
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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 ...
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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. ...
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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 ...
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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 ...
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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
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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, ...
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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 ...
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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. ...
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0answers
92 views
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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
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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
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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 ...
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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
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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 ...
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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
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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 \...
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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 ...
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1answer
51 views

Give NeumannValue a nonlinear function

I have the following simpler example of my actual problem which reproduces my question ...
3
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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 ...
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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 ...
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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: ...