Questions tagged [boundary-conditions]
The boundary-conditions tag has no summary.
386 questions
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Oblique derivative boundary conditions in FEM
In one of my tasks, it is necessary to set a boundary condition in the form of an oblique derivative for the two-dimensional Laplace equation.
Do you know how this can be done in Wolfram Mathematics? ...
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How to make DSolve obtain this solution to this IVP first order ODE?
V 14.3 can not solve this IVP(Initial value problem) first order ode from textbook
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Why does the "No Dirichlet condition" warning appear for fine mesh but not for coarse mesh?
It is known that the solution of the Laplace equation with exclusively Neumann boundary conditions is ambiguous. Wolfram Mathematica warns about this by submitting messages like this one:
No ...
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Greenfunction of 1D Helmholtz Equation
I'm new to Mathematica, and I'd like to find the Green function of the 1D Helmholtz Equation
$$ \frac{d^2}{dx^2}u + k^2u=\delta(x-x_0)$$
on the whole x axis.
I know that there are a few possible ...
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Why do different boundary condition formulations in ParametricNDSolveValue give different results with FEM warning?
I'm solving a coupled system of differential equations for neutron star matter using ParametricNDSolveValue. I encountered two issues:
Boundary Condition ...
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How to apply a pressure load to the surface of a deforming mesh?
I would like to be able to apply a pressure load to the surface of a thin membrane for FEM, and wish to make sure that the pressure always acts in the direction of the normal vector of the surface of ...
- 4,677
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76
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pdetoode for heat equation with Neumman bc without NeumannValue
I want to try pdetoode for solving a heat equation with Neumman bc without using NeumannValue. I modified this code:
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139
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Extend of numerical ODE for a special case [duplicate]
I want to continue the plot but I don't know how to do it?
...
- 475
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258
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Why does NDSolve fail to converge when solving for Sadowsky ribbon with nonzero θ?
I am working with the control equations of a Sadowsky ribbon, where the basic equations eqs and boundary conditions bc0 and <...
- 366
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Lagrange's method applied to Earth-Sun system using NDSolve. Problems: Earth too fast and CM not (almost) centered [closed]
Good morning to all! I am trying to solve the two body problem for the Sun-Earth system. I make use of the Lagrangian Method and NDSolve; code is shown below:
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NDSolve: Prescribe a linear constraint on a boundary
This is a representative volume element problem on a unit square.
I would like to apply the following linear constraint on a boundary:
$u(x,1)=u(x,0)+0.3$
How can do this? There seems to be no way. ...
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Unable to solve set of partial differential problems (coupled)
First, I'd like to apologize for any mistakes as this is my first time asking this question. I have a set of PDEs, and I am unable to solve them using NDSolve in ...
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210
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Finding the best initial condition of NDSolve for different boundary condition
I have the following Mathematica code, which solves the second-order differential equation:
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274
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Solving a second order differential equation with parity symmetry
I am trying to reproduce the Figure 2 from this paper.
The code that I am using to solve the differential equation is given below:
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Imposing boundary conditions on coupled ODE solutions symbolically to solve for constants
I'm trying to solve symbolically these two ODEs:
$$ \begin{array}{ll}
\eta_1 \frac{1}{r} \frac{\mathrm{d}}{\mathrm{d} r}\left(r \frac{\mathrm{d} u_1}{\mathrm{d} r}\right) = P_1, & r \in[0, \alpha]...
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NDSolve the 1D Poisson Equation on a Periodic Domain
I want to use NDSolve on the simple equation
$$ q'' == g(q,h) $$ for some function $g$ on the domain $ \Omega=[-1,1]$
with periodic boundary conditions $$ q(-1)=q(1) \text{ and } q'(-1) = q'(1)$$
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Unconventional Boundary Conditions
A follow up from the previous question
References: similar question, paper
Constants
My domain is $\Omega$ = Rectangle[ {xmin, ymin} , {xmax,ymax}]
xmax >> ymax, xmin << ymin
Assume all ...
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NDSolve can't find Neumann Value on domain
Trying to solve for the temperature around an axisymmetric thin disk. Edges of the domain are DirichletConditions which work fine, but the solver can't find the <...
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Boundary condition error with 2D Poisson equation
I'm trying to solve Poisson's equation for the temperature difference ($\Delta T$) between two layers with known conduction between them. The layers have conductive elements spaced in a hexagonal ...
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130
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How to Solve a DAE System with Integral Constraint and Moving Boundary in Mathematica?
I am currently working on solving a DAE system in Mathematica, which includes an integral constraint and a moving boundary. I have attempted to use ParametricNDSolve, but it doesn't seem to work for ...
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285
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Boundary conditions issue with Laplace equation
I'm trying to solve the Laplace equation for two spheres of radius rs raised to a potential of 1 a distance l away from each ...
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2d diffusion equation with boundary conditions: problem with probability conservation
Version: Mathematica 12
I want to numerically solve the 2d diffusion equation $\partial_t u(x,y,t) = D\Big( \partial_x^2 u(x,y,t)+ \partial_y^2 u(x,y,t) \Big)$ over some region with specific boundary ...
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Young Laplace equation with shooting method
I am attempting to follow the method outlined in this paper on page 5, where the first step requires solving a 2 point boundary value problem. I have tried using the Shooting Method, but to no avail.
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I have a problem with this code because it is time invertible symmetric but it is not working
I have this code I want to check for a numerical solution. I get the same shape. The function $y$ is an invertible in time so I plot $y[x]$ and $p[t]$. The $p$ function should decrease but it isn't ...
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Using numerical method to go backward for ODE [closed]
I want to use this code for the backward Numerical solution but patently not well defined?
...
- 475
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2
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165
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Numerical and analytical solutions do not agree [closed]
Hi everyone could anyone have look why this code is not running?
...
- 475
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1
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232
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Partial differential equation with derivatives respect to two variables
I am trying to solve the following set of equations in the interval $0<t<1$ and $0<y<1$
$\partial_t a(y,t) + \partial_y[ a(y,t) u(y,t)]=0,$
$\partial_y[ a(y,t) \: (m+ 3 \frac{\partial_y u(...
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Boundary conditions being ignored or not obeyed by NDSolveValue
I have the following coupled ordinary differential equations (drift-diffusion with a loss term) that I am having trouble with solving. One of the boundary condition I supply is being ignored. When I ...
- 2,907
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Solving difficult coupled PDEs with DSolve
I have used mathematica to find a set of dynamical equations with boundary conditions. I wonder if it's possible to solve these equations with DSolve. Could anyone help me with this?
Here are my sets ...
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Issue with solving coupled partial differential equations with NDSolve for certain boundary conditions
I am trying to solve the coupled PDEs for functions u, v and w.
The main problem I am facing is that I am unable to understand how to input boundary condition of this type in NDSolve:
D[u[x, y], y] + ...
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Any ideas on how to use NDSolve to solve this nonlinear 2nd order ODE
I can't get to work this code to solve a nonlinear second order boundary value problem.
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Boundary сonditions specified in different domains
I am modeling mass transport phenomena involving convection and diffusion within a two-dimensional box. The box has a height ranging from 0 to h along the y-axis and is divided into two domains along ...
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How to constrain two PDE variables to be the same value on boundary?
I have a 4 pdes for 4 variables: v, v2, ua, and p. I would like to specify that v==v2 on the left and right boundaries at all times. Here are the equations:
I discretise the system using PDEtoODE. ...
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How to solve electric drift and diffusion PDE using `NDSolveValue`?
I am trying to learn how to use NDSolveValue with various boundary conditions. After going through several examples here, I thought I'd try it on what I thought ...
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How to solve the integro - differential equation with complex value involved?
I am trying to solve the PDEs which contains Integro-differential and complex values.
For example, the following PDE can be easily solved.
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NDSolve fails first order ODEs, but works when transformed to second order [duplicate]
The short version is that I am trying to solve a relatively simple system of coupled first order ODEs with NDSolve in Mathematica 12.1.1.0 on Windows. This system ...
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Solving system of coupled pdes with Neuman and Drichlet Bc
I am trying to solve a system of coupled PDEs. However, I have issues assigning initial and boundary values to the unknown field. I have checked and initial values satisfy the boundary conditions, and ...
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1
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EM Wave Equation: Insufficient initial conditions for NDSolve?
I am trying to model a EM wave propagation through a region of free space. However, Mathematica tells that there are insufficient initial conditions, even though I specify all values at ...
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3
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2
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104
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RSolve does not evaluate this recursion with two boundary conditions
I am using RSolve to solve for a function defined recursively, with two boundary conditions:
First boundary condition describes the relationship between $f(1)$ and $f(0)$
Second boundary condition ...
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2
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1
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257
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NDSolve: how to solve "ndnum error"
I have a problem of finding the shape of a current. please see the details here NDSolve does not accept the boundary condition
I wrote a code but it gives the "ndnum" error. I tested the ...
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NDSolve does not accept the boundary condition
I am new at Mathematica and trying to solve a nonlinear PDE with the help of NDSolve.
H, the height of the current is a function of x and t. Based on the context I know the current has a parabolic ...
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Piecewise BVP not working on interval for NDSolve [duplicate]
My Mathematica skills aren't the best but this solution isn't making sense considering the boundary value I am supplying.
The leftmost boundary condition, i.e. at $x=0$, $c[t,x]$ should be $1$ for $t\...
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Cavity resonator modeling with Wolfram Mathematica
I am attempting to determine eigenfrequencies and the corresponding electric field distribution in a rectangular cavity resonator with perfectly conducting walls. In the simplest case of a rectangular ...
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How can I use a loop inside a boundary condition in NDSolveValue?
How can I use the variable i of a "do" loop inside a boundary condition in NDSolveValue, and plot the solution for ...
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Solving BVP using shooting method and plotting the result
I am not able to obtain any plot with the following code.
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121
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1
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How to set up "mixed" boundary conditions for NDSolve for PDE? [closed]
I have the following PDE that I am able to solve using DirichletCondition with NDSolve as the following:
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