Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
271
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Using DSolve, For A System With A Piecewise Function, And For Given Boundary & Continuity Conditions
I'm trying to solve a system of ODE's, analytically, to find the integration constants.
The system is the following (with zUpper=125 000 and zLower= 200 000).
For 0 <= z <= zUpper:
3 T''[z] == 0....
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Numerical solution of differential equation with DiracDelta fit boundary condition at zero poorly
I need to solve: $x^2y''(x)+(2x+1)y'(x)-x^2\omega^2y(x)=\frac{-\omega^2\delta(x-x_0)}{4\pi},x\in[0,\infty)$ with boundary conditions:$y(0)=1,\ y(\infty)=0$ , $\omega$ is a function of this form: ...
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Using NeumannValue in finite element method to replace a derivative boundary condition in NDSolve to overcome a computational overflow
I am trying to implement and evaluate the function GeneratePsiOfX. The definition of GeneratePsiOfX is:
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Solving a 2D recurrence diagonal-by-diagonal
I have a 3D recurrence relation -- which I know can be hard for Mathematica to work with, so I boiled it down to 2D.
We have two functions, $f_1(i,j)$, $f_2(i,j)$ defined on the state space $\{(i,j) | ...
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Simulating the Response of Charged Particles to Apertures with Inhomogeneous Electric Fields Passing through them
I have produced a simulation which allows me to observe a static electric field produced by a charged plate as it passes through some complex apertures in a different, oppositely charged metal plate.
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2
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Defining Dirichlet Boundary Conditions on an Imported 3D Object with Apertures in it
I am trying to simulate a static electric field (in 2d and 3d) as it passes through a couple of apertures in a 3D "metal sheet" (model imported as a .obj file) given here:
https://www....
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Solving second order non-linear DE with boundary condition
I was trying to get some result from this equation but I can't find the solution. please see what is wrong with it??!! thanks
f, s are positive and k will be negative or positive.
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271
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NDSolve for Laplace equation on disk is not working
I want to solve the laplace equation on the disk using NDSolve.
Particularly I want to solve the problem $$\frac{\partial^2 u }{\partial r^2 } +r^{-1}\frac{\partial u }{\partial r }+r^{-2}\frac{\...
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2
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The solution for Sinh[] and Cosh[]
I saw this equation a book that has two solution: one Sinh[] and another one is Cosh[] but I can't find them with Mathematica 13?!!
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FEM: modelling 2D flow under periodic forcing
Despite many examples of periodic boundary conditions being presented, it remains difficult to obtain a periodic solution. Let us consider a simple example of a flow in a two-dimensional channel under ...
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56
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Numerical Plot for an example
I would like to compare the numerical and analytical solution with plot for this example but something is wrong I don't know how to fix it?!!
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153
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Using Neumann boundary conditions for the wave equation
I have the following code to solve the wave equation in 2D:
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80
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RSolve two variables with multiple boundary conditions
In short, I want to solve a recurrence equation in two variables with multiple boundary conditions.
In more detail:
For instance, suppose I want to compute
$a[0,j]= 1 \quad \forall j$
$a[i,0]= 1 \quad ...
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RSolve with two boundary conditions
I want to solve a recurrence equation that has boundary conditions on both sides:
$a[0]= 1$
$a[n]= 10$
$a[i] = a[i-1]-a[i+1]\quad \forall i \in \{1, \ldots, n-1\}$
This should be a well defined ...
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How to use 2D DSolve over unit disk with Dirichlet boundary?
I'm trying to solve a 2D PDE with homogeneous Dirichlet boundary condition.
The problem I'm actually trying to solve is a bit more complicated, but I came up with a reduced version just to get DSolve &...
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Plot an example for some functions
Today I just wanted to run this code but I have some difficulty if you can have a look?
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Ploting a function
I just ploted y[x],y'[x] but I would like to plot other function which is g[x] based on my solution but it can't plot this ??!!
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Solve a differential eq with a boundray condtion and plot it
I just wanted to know how to plot this for different value of a,b and f (Table[])?
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Solving 2D Landau-Khalatnikov equation & Poisson equation using finite element approach
I would like to solve Landau-Khalatnikov (LK) equation and Poisson equation using finite element approach to simulate ferroelectric hysteresis loop, electric potential distribution and electric ...
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Solve symbolic ODE with symbolic initial condition
I have the following ODE
c + (p + r) y[p] == p (u + (-1 + p) y'[p])
where car and u are parameters of the problem. I want to solve the ODE using a symbolic initial condition y(0)=x for some x, or also ...
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Solve 1d fractional parabolic equations with Mathematica
How can we use Mathematica to solve the following fractional parabolic problem?
$$\partial_t u(t,x) +a(-\Delta)^su(t,x) + bu(t,x)= f(t,x) \quad t >0, \ x \in (\alpha,\beta),\\
u(t,x) = u_c(t,x)\...
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Solve and Plot an example with boundary condition
I have this piece of code to plot this solution, but I guess it should be numerical or parametric way!!!
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Solve 1d fractional equation with Mathematica
How can we use Mathematica to solve the following fractional elliptic problem?
$$a(-\Delta)^su + bu= f(x) \text{ in } (0,1),\\
u = c \text{ in } \mathbb{R} \setminus (0,1), $$
for $a,b,c\ge0$ and a ...
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simple question for 2 order DE
I want to get some plots from this equation under any boundary condition(y[0]=0,y'[0]= 0)!! but I guess there is some singular point.
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The second order differential equation non-linear case [duplicate]
I'm working to solve this equation but it's not giving me anything
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Numerical Solution for this equation [closed]
I want to solve this equation in Mathematica then plot x[t]:
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Plot and DSolve [closed]
I'm working on this code to modify it but I can't plot it and solve the second part?!!
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I don't know how to get a solution to this differential equation
I work on this equation I don't know how to get some a solution from second part becuase it just gives me some unknown lines, first part is easy and I just put it for next part.
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Plot and Table in the same line
I would like to plot this with different y1 but isn't working!!
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ParametricPlot3D Curve and ImplicitRegion: Projections and Intersections
There is a parametric 3D-Curve:
ParametricPlot3D[{Sin[t], Cos[1 - 3 t], Sin[2 t - 1]}, {t, 0, 10}, BoxRatios -> {1, 1, 1}, AxesLabel -> {x, y, z}]
And ...
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Inverse Function for an example
I have this funtion i would like to calculate the inverse
Inverse[Sqrt[1 - Cosh[2 t] + a Sinh[2 t]]]
a is positive number.
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Dirichlet condition from user-defined polygon
I would like to specify a Dirichlet condition from a polyhedron defined by a set of points.
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Syntax Problem In NDSolve with Free Boundaries
I am considering a problem with two free boundaries. When I consider the equation:
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Switching boundary conditions in NDSolve
I am having a syntax problem in solving a second order non linear differential equation. When I specify the command:
...
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Periodic and non-periodic boundary condition in PDE
I tried to simplify a complicated PDE to understand what's going wrong, but even the simplest form is not fully accepted by Mathematica and does not work completely.
Please take a look at this:
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The Range of a Function
I would like to see minimum and maximum for this example!
g[x_]:=(3 a - 2)/((2 + 3 b - 3 a) x^2) + f*x^(-3 a + 3 b + 2)
also for those parameters "1 < a &...
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Solution of a BVP by Means of DSolve [closed]
If we consider the BVP $y^{\prime\prime}(t)=\frac{3}{2}y(t)^{2}$ where $0\leq t\leq1$ and $y(0)=4$ and $y(1)=1$. Then its solution is $y(t)=\frac{4}{(1+t)^{2}}$. I have set the BVP above as in ...
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Solving and plotting a differential equation
I was trying to solve and plot this equation but the solution it is not clear !!!
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Solving coupled ODE by analyzing solution near zero
This question is related to an earlier question I had asked, regarding coupled first order odes. I'll add the system of odes with their boundary conditions again here. .
The comments for the previous ...
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Two Coupled First Order Differential Equations
I'm trying to solve the following differential equations. The 4 boundary conditions imposed are based on physical grounds required for regularity at the origin. It is known that these equations do not ...
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Reciprocating flow in a channel over a heated surface
The following is a coupled heat transfer and fluid flow problem.
A thick plane channel is being heated with a constant flux from the bottom (at $y=-e$) with a constant heat flux $q$ as shown in the ...
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Plot the solution and Inverse as well
I used this code to solve an equation and now I would like to plot the solution with its inverse. I can't get some figures?!!
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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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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 $r\in[0,10]$
$$ \left(\partial_t^2 - \frac{1}{r^2}\partial_r r^2 \partial_r \right) \theta(t,r) = -(1+2\Phi(...
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NDSolve gives different result if I use NeumannValue to set initial condition
While trying to get familiar with the NeumannValue function I tried solving the wave equation on $r\in [0,2\pi]$ for $\theta(t,r)$
$$\partial^2_t \theta - \partial^2_r \theta =0, $$
with intial ...
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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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