Questions tagged [boundary-conditions]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
30 views

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....
user avatar
0 votes
1 answer
70 views

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: ...
user avatar
0 votes
0 answers
61 views

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: ...
user avatar
1 vote
0 answers
62 views

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) | ...
user avatar
  • 251
1 vote
0 answers
69 views

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. ...
user avatar
  • 311
3 votes
2 answers
99 views

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....
user avatar
  • 311
0 votes
0 answers
57 views

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. ...
user avatar
6 votes
2 answers
271 views

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{\...
user avatar
  • 173
2 votes
2 answers
395 views

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?!! ...
user avatar
4 votes
0 answers
102 views

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 ...
user avatar
0 votes
1 answer
56 views

Plot for DSolve in mathematica [closed]

I don't Plot it's not working!!, can you help me? ...
user avatar
0 votes
1 answer
65 views

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?!! ...
user avatar
4 votes
2 answers
153 views

Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
user avatar
0 votes
1 answer
80 views

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 ...
user avatar
  • 251
2 votes
2 answers
156 views

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 ...
user avatar
  • 251
0 votes
1 answer
72 views

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 &...
user avatar
2 votes
1 answer
55 views

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? ...
user avatar
1 vote
2 answers
80 views

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 ??!! ...
user avatar
3 votes
2 answers
104 views

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[])? ...
user avatar
6 votes
1 answer
255 views

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 ...
user avatar
  • 63
1 vote
0 answers
84 views

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 ...
user avatar
  • 53
3 votes
1 answer
147 views

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)\...
user avatar
  • 269
1 vote
1 answer
67 views

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!!! ...
user avatar
5 votes
1 answer
126 views

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 ...
user avatar
  • 269
2 votes
1 answer
73 views

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. ...
user avatar
0 votes
0 answers
21 views

The second order differential equation non-linear case [duplicate]

I'm working to solve this equation but it's not giving me anything ...
user avatar
0 votes
1 answer
137 views

Numerical Solution for this equation [closed]

I want to solve this equation in Mathematica then plot x[t]: ...
user avatar
0 votes
1 answer
71 views

Plot and DSolve [closed]

I'm working on this code to modify it but I can't plot it and solve the second part?!! ...
user avatar
2 votes
2 answers
86 views

Inverse of an Animation

I was thinking, it's possible to plot inverse an animation?? ...
user avatar
0 votes
0 answers
97 views

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. ...
user avatar
2 votes
1 answer
69 views

Plot and Table in the same line

I would like to plot this with different y1 but isn't working!! ...
user avatar
1 vote
2 answers
110 views

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 ...
user avatar
  • 1,847
1 vote
2 answers
45 views

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.
user avatar
1 vote
1 answer
79 views

Dirichlet condition from user-defined polygon

I would like to specify a Dirichlet condition from a polyhedron defined by a set of points. ...
user avatar
  • 145
1 vote
1 answer
74 views

Syntax Problem In NDSolve with Free Boundaries

I am considering a problem with two free boundaries. When I consider the equation: ...
user avatar
  • 11
0 votes
0 answers
39 views

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: ...
user avatar
  • 11
1 vote
1 answer
91 views

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: ...
user avatar
  • 135
0 votes
1 answer
116 views

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 &...
user avatar
1 vote
1 answer
106 views

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 ...
user avatar
  • 169
2 votes
2 answers
162 views

Solving and plotting a differential equation

I was trying to solve and plot this equation but the solution it is not clear !!! ...
user avatar
2 votes
1 answer
119 views

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 ...
user avatar
  • 73
1 vote
0 answers
118 views

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 ...
user avatar
  • 73
10 votes
2 answers
543 views

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 ...
user avatar
  • 143
1 vote
2 answers
166 views

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?!! ...
user avatar
3 votes
1 answer
191 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 ...
user avatar
  • 143
1 vote
1 answer
97 views

Non- linear ODE

I was working on this equation but I can't get out something for this: ...
user avatar
1 vote
0 answers
66 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(...
user avatar
  • 367
2 votes
0 answers
93 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 ...
user avatar
  • 367
1 vote
0 answers
115 views

A Simple equation [closed]

I don't know why is not working?!! ...
user avatar
5 votes
0 answers
98 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 ...
user avatar
  • 8,558

1
2 3 4 5 6