Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
327
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R-K fourth order scheme for system of ODEs containing 32 differential equations
In the present code, I am trying to solve the system of differential equations using the R-K fourth-order scheme. I am trying to plot the function u and T, but it is showing some error in the boundary ...
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2
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126
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Spherical Heat Equation and Convection Boundary Conditions
I'm trying to solve transient heat conduction equation in spherical domain in Mathematica. I made the simplifying hypothesis that temperature varies only with time and radial coordinate.
The code is:
<...
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0
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29
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NDSolve diverges with Neumann boundary condition [duplicate]
I am solving Poisson-like PDE with the Finite Element Method in Wolfram Mathematica. Only the Neumann boundary condition is imposed on the boundary. Of course, the solution is not unique, most likely ...
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Graph plotting using system of ODE with NDSolve command
In the present question, I am trying to solve a system of ODEs with corresponding boundary conditions. And then, trying to plot the velocity function, but it shows some errors. Can anyone please help ...
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3
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Solving a one-dimensional free-boundary problem with a singular boundary condition
Addendum (orginial question below). Thank you for the responses! After thinking some more about this problem, and thanks to @bbgodfreys helpful comment, I realised that the problem as posted below is ...
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How to accelerate FindRoot?
Original:
I am running the following code to find the root of F , T and MM, here is an example
...
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0
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On formulating a Neumann boundary condition
I am attempting to follow this tutorial in the documentation on using FEM to solve PDEs. I am having difficulty understanding how to formulate the Neumann boundary condition for my free-boundary ...
- 155
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86
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Solving a Variable Number of Difference Equations with RSolve
I'm trying to solve a variable number of linear equations defined by
$$
\begin{align} x_0 &= A+Bx_1 \\ x_i &= C+\frac{B}{2}(x_{i-1}+x_{i+1}), \hspace{.25cm} 1\leq i \leq n-1 \\ x_n &= C+...
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Plotting of graph after solving system of ODEs using NDSolve command
In the present question, I am trying to solve a system of ODEs with corresponding boundary conditions. After that, I tried to find Q, which is firstly dependent on z and then on M. Then, after using ...
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Can Mathematica's FEM solve coupled Dirichlet Boundary Conditions?
I am solving a coupled system of PDEs using Mathematica's FEM capabilities.
Specifically, the Navier-Stokes equations with a no-flux stress-free boundary.
To do this, I need to specify a Dirichlet ...
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How to minimize numerical error in the code while solving the system of ODEs
I just want to ask in the graph of the code mentioned in the link, while plotting u from {-0.0001,y,0.0001}, the jump is coming because of the numerical error u1-u2. Can anyone please tell me, how to ...
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differential wave equations [closed]
By seeking a solution of
∂u
∂t
= c
2
∂
2u
∂x
2
in the form u(x,t) = X(x)T(t), obtain and solve ordinary
differential equations satisfied by X(x) and T(t). Hence write down possible solutions for
u(x,t)...
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1
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213
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Solving a system of ODE using shooting technique with NDSolve command
In this code, I am trying to solve a system of first-order ODE with corresponding boundary conditions. But it is showing some error which I am not able to rectify. Can anyone help me in rectifying the ...
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101
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Problem with PDE boundary and initial conditions
I am trying to numerically solve the following PDE
...
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116
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Implementing and testing boundary conditions in polar coordinates for convection-diffusion equation
I am modeling a system using the convection-diffusion equation on a 2D, radially symmetric space. I wanted to do some sanity checks to make sure I am coding it correctly. I set up a situation where I ...
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Get the value of boundary point
I used the $NMinimize$ instruction to calculate, but what I got was the dt value of the red circle. If I want to obtain the dt value of the green circle, how do I obtain it?
The code for generating ...
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202
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How to model partial wavefunction collapse when part of a wavefunction hits a barrier?
This code models a complex Gaussian wavefunction expanding from the origin, part of which hits a barrier at x=10, Abs[y]<15. The code shows the wavefunction reflecting off the barrier, which is ...
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How to deal with differential algebraic equation (DAE) in ParametricNDSolve?
I have the following system of 10 differential equations where the first two equations are algebraic for u[t] and srz[t]. We ...
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4
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201
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Solving PDE with power series
I would like to solve the PDE
$$\partial_{x}f(x,y) + f(x,y)^2 = g(x,y)$$
with $f(0,0)=0$ and $\partial_y f(0,0)=0$ using a power series ansatz, i.e. I have an explicit expression for $g(x,y)=\sin(x+y)\...
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163
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Drift-diffusion ODEs with two boundary conditions
I am trying to solve drift-diffusion equatons (Poisson's equation, continuity equations for electrons and holes and Kirchhoff's equation) for a reversely biased diode in a stationary state (no time ...
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164
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Solution to a 2D Schrödinger equation
I am trying to solve a 2D Schrödinger equation with a complicated non-separable potential $V(z,\rho)$,
$$ \nabla^{2}\Psi(z,\rho) +2(E_{0}-V(z,\rho))\Psi(z,\rho),$$
where $E_{0}$is the energy, $\hbar=m=...
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Invalid PeriodicBoundaryCondition for Navier Stokes problem using NDSolveValue
Background: I'm looking to have a 2D re-entrant channel of a geophysical flow that is forced by a wind stress at the surface ("taux"; below) and experiences planetary rotation ("cor&...
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147
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Setting up a PDE for a time-independent Schrödinger equation
I am trying to solve a 2d Schrödinger equation with a non-separable potential because I want to calculate the probability of reflection for different angles of incidence of a plane wave.
Here I ...
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2
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192
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Stefan problem with mixed bc
I am trying to solve through Mathematica the classical Stefan problem
$$
\left\{
\begin{array}{lll}
\dot{v}(x,t)=v_{xx}(x,t) & x\in(0,s(t))\\
\dot{s}(t)=-v_x(s(t),t) & x = s(t)\\
v(0,t) = 0 &...
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71
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Non-minimal coupling ξ , Minkowski false vacuum decay case (shooting method) (An update to the previous question)
I asked a few days ago this question:
Non-minimal coupling ξ - numerical bounce solutions (shooting method, false vacuum decay)
Alex Trounev helped me improve my code building based on this paper (...
2
votes
1
answer
137
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NDSolve with parametric endpoint
I want to solve numerically a system of ODEs of the form:
$$\ddot{y}+3\frac{\dot{b}}{b}\dot{y}=2Cy(y^2-1)$$
and
$$\dot{b}^{2}=1-b^{2}+\frac{D}{2\sqrt{C}}b^{2}\left(\dot{y}^{2}-C(y^{2}-1)^{2}\right)$$
...
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2
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Constraints in a set of equations
I am currently working on a system of equations that is subject to a determinant constraint. Specifically, I have a matrix $B$ with $\det(B) = 0$, and I aim to construct a linear combination of its ...
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Non-minimal coupling ξ - numerical bounce solutions (shooting method, false vacuum decay)
I have the potential below:
$$V(\phi)=-\frac14 a^2(3b-1)\phi^2+\frac12 a(b-1)\phi^3+\frac14 \phi^4 +a^4c$$
This potential has 2 minima, the false vacuum $\phi_f=0$ which tunnels to the global minimum, ...
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148
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DSolve solution for 1st order PDE involving complex number does not match initial condition
Bug introduced in 11.3 or earlier, persisting through 13.2.1.
[Mathematica 12.0.0.0, MacOS X x86 (64bit)]
Trying to solve
...
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73
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How to solve boundary value problem?
Is it possible to solve a boundary value problem like this?
...
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129
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How to specify derivative boundary conditions for the gradient to be normal to the boundary?
I'm currently modeling an electric field with 2 charges. To do so, I use NDSolveValue to solve a Laplacian with 2 Dirichlet conditions on the voltages of the ...
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Shooting technique using NDSolve
Here I am attaching my code below. It took all the variable's values, but the graph window was empty. I am not able to recognize, where is the error exactly. Differential equations were also, checked ...
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Shooting technique [closed]
Here is my code, I am trying to plot the graph of the differential equation, But output graph is an empty window. can anyone please help in getting the graphs. This equation is a modified bessel ...
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Difference Equation with Upper Boundary Condition, Lower Terms Not correct
I am struggling to understand the solution Mathematica is providing for the following recurrence relation
As I have written a[i] I expected the following behavior
<...
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0
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Implementation of Neumann-like boundary condition
If we wish to solve an elliptic PDE, say $\nabla^2\phi=\text{given}$, on a domain $\Omega$ with Neumann boundary conditions, $\hat{\mathbf{n}}\cdot \nabla \phi\Big|_{\partial \Omega}=\text{given}$, ...
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Plotting the solution of an equation
I just wondering if I can plot this solution?
FullSimplify[Integrate[1/Sqrt[-1 + f/3 x^2 + b/x], x] , Assumptions -> {x > 0, f > 0, b > 0}]
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Solve an equation for different values
I was trying to solve this equation for different value of a constant (a) but the solution is not different for those values?!! b and m are positive values.
...
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160
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Unstable boundary values using NDSolve?
I have an equation:
w1[u_]=-(1/2) u^2 ea e0 Sin[2 a[z]] + K (a''[z])
with numerical values,
...
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2
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362
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How can we apply specific boundary conditions with NDEigensystem?
I'm solving an eigenvalue problem with special b.c. mentioned in the paper Edge states in gated bilayer-monolayer graphene ribbons and bilayer domain walls. (See Eq.(3)(6)(7) and the paragraph after (...
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False vacuum bounce solution (curved space) shooting method problems
Merry Christmas, I think I can still say it. I am back this time for my problem in a simpler case, without coupling. I have a problematic code now and I want your help. I want to solve numerically the ...
2
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2
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NDSolve Extrapolating boundary conditions for FiniteElements
I'm trying to solve a 1+1 (1d time + 1d space) partial differential diffusion equation.
My NDSolve call look basically like this:
...
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Coiling of flexible ropes (nonlinear BVP of ODEs with 10 unknown functions and 2 parameters)
I want to solve this ODEs with NDSolve, but it fails. The $F$(F), $\gamma$ (γ) is the given ...
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1
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Solving Laplace PDE in mathematica
I'm trying to get the general solution for the Laplace equation: $\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0$ on the domain $\mathbb{R_0}\times\mathbb{R^+}\backslash\{(0,...
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Numerical solution of a partial derivative problem
WARNING: a couple of days ago I posted a similar question, but due to the impossibility of DirichletCondition[] to handle "cross-coupling of dependent ...
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4
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278
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I want to plot the solution but
I want to plot this solution for the different value of d and x but it is an Elliptic function.
...
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3
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205
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First order Differential equation with boundary condition
I'm wondering why it is not solving with the Mathematica??
...
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155
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Different answer using Dsolve or NDSolve to solve a PDE
I'm working on getting a numerical solution for the following PDE:
$$
u_t-u_{xx}=0,\ x\in[0,1], t\in[0,1],\\
u(x,0)=\sin(2\pi x),\\
u(0,t)=0,\\
u_x(1,t)=2\pi e^{-t}.
$$
The hand solution for this PDE ...
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Coupled PDEs with different dimensions and boundary conditions
The geometry of the problem is described by a cylinder inside a rectangular domain. The equations describes the region in between them.
I have 2 PDEs for U(x,y,z) in the bulk region and V(z) for -0.5&...
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