Questions tagged [boundary-conditions]

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2answers
64 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
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3answers
242 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 ...
8
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3answers
335 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
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1answer
75 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
91 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
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1answer
363 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
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1answer
34 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
73 views

the question about second order differential equations

I have a second order differential equation with two known initial conditions like this: ...
3
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1answer
295 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
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1answer
82 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
122 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
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1answer
58 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
45 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
46 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
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2answers
493 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 ...
4
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2answers
157 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
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2answers
189 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
63 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
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1answer
84 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
59 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
82 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
54 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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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 ...
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0answers
67 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
134 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
50 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
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1answer
143 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
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0answers
91 views
0
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0answers
82 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
67 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
38 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
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1answer
101 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
314 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
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1answer
127 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
612 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
39 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
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1answer
49 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
140 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
80 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
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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: ...
1
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0answers
234 views

General:: Exp[-717.401] is too small to represent as a normalized machine number; precision may be lost

I am solving pde. For the post processing bvp, there is solution given in output which is the solution from mathematica version 10.0.1. Output from above in mathematica 10.0.1 is, But when the similar ...
0
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0answers
115 views

Solve coupled partial differential equations with absorbing BCs

I try to solve the following system of coupled equations with NDSolve but the results seem to be not correct. I attached my code in which five dependent variables $f_{1}$, $f_{2}$, $f_{3}$, $f_{4}$, ...
2
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0answers
165 views

Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \begin{equation} \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
7
votes
3answers
615 views

Solving heat equation on a cylinder with insulated ends and convective boundary conditions

I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
1
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0answers
96 views

PDE with boundary condition (differential equation)

I am trying to find a solution to this boundary value problem $$h_t= \frac{1}{2} \sigma^2 x^2 h_{xx} + r x h_x \quad s.t.\\ Ah(b,t)+Bh_x(b,t)=g(t),$$ where $A,B,\sigma,r,b$ are constants and $g(t)$ ...
4
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3answers
268 views

Geometrically nonlinear beam deflection

Edit only for those interested in large deflections of beams I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
0
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2answers
110 views

Error when using NDSolveValue. Lists are not the same shape

Please, help me with the following issue. I am solving the following system of the coupled PDEs with the following boundary conditions and initial conditions. After performing the following ...
1
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0answers
60 views

NDsolve Boundary Condition is a Function of the Solution

I am trying to solve something like Fick's Law using NDSolve: $$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$ Subject to a ...
3
votes
1answer
103 views

Shooting Method with extra Unknown Condition

I've been trying to solve a system of 3 coupled 2nd order ODEs, for a real variable $x$, $0\geq x\leq \infty$. The equations are the following: \begin{align} &x^{2}\,h''(x) - x\,h'(x) + x^{2}\,g^{...
0
votes
0answers
75 views

solving a 2D eigenvalue problem for a partial differential equation

I'm fairly new to Mathematica and I'm looking for a way to solve a partial differential equation subject to periodic boundary conditions. The form of the equation looks like this: $\frac{\partial^2}{\...