Tag for questions solving partial differential equations (PDE) with Mathematica. This tag is suggested to be used together with tag "differential-equations".

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6
votes
1answer
114 views

Long running ToElementMesh with very “large” domains

I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. Just that the domains has a big ...
20
votes
2answers
376 views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
2
votes
1answer
97 views

PDE: Solving Burgers' equation with initial value given by a self consistency equation

I would like to solve in Mathematica the well known inviscid Burgers' equation \begin{align} \begin{cases} u_t(x,t) + u(x,t)u_x(x,t)= 0 \\ u(x,0) = m(x) \end{cases} \end{align} where $$m(x) ...
14
votes
2answers
183 views

Least effort to handle a point source inside the domain of PDE(s)

By point source I mean a constrained condition at one point inside the domain of PDE(s). For example: $$\frac{\partial ^2u(t,x,y)}{\partial t^2}=\frac{\partial ^2u(t,x,y)}{\partial ...
1
vote
0answers
50 views

Dirichlet conditions being ignored

I have the following domain: ...
1
vote
1answer
63 views

Toroidal implicit region looks weird

I have the following toroid surface: ...
7
votes
3answers
241 views

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
5
votes
0answers
82 views

Alternatives to FiniteElement as Spatial Discretization Method for NDSolve

Finite Element Programming: [...] It is possible to skip this section and continue with the discretization stage and make use of the initialized data structures ...
2
votes
1answer
102 views

Trouble understanding NeumannValue and Inactive/Formal PDEs

I read all documentation about the Finite Element Method in Mathematica 10, and I read some questions here, but I'm still unable to properly understand how to use the ...
5
votes
3answers
112 views

Trouble Discretizing a ParametricRegion; Joukowsky Map and Wing Profiles

I'm trying to compue a mesh of full 2D region delimited by the a circle transformed with a Complex map. ...
9
votes
2answers
328 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
0
votes
0answers
50 views

when DSolve fails

I am doing this mathematical problem $c*G_{vv}+ d*G_{u} + e*G_{v} +f*G=0$, where $c, d, e$ and $f$- are constant coefficients. I already know that this is second order PDE and we classify it by ...
0
votes
0answers
65 views

Solving PDE with conditions

I am new to Mathematica, so it maybe a silly question. So, I'm trying to solve the following PDE with Mathematica: $u=u(x,y)$ $\partial_x ^2 u-6\partial_x \partial_yu+9\partial_y^2u=x^2+y^2$ ...
2
votes
0answers
129 views

NDSolve and strange “nonlinear coefficients problem”

I'm stuck solving the following problem. I defined two functions as follows: $$ \varphi(\lambda) = \frac{\left((\lambda-2)^2-1 \right)^2}{4}$$ $$ \gamma(\lambda) = \varepsilon^2 ...
4
votes
1answer
128 views

Non-separable partial differential equation in polar coordinates

I'm trying to solve the Schroedinger equation in 2D for a system interacting via a dipole potential. This means, in effect, I'm trying to solve the nonlinear PDE $$ -\frac{1}{r} ...
0
votes
0answers
61 views

Help deciphering Neumann Value

Version 10 has an option for NDSolve called "NeumannValue" which is supposed to allow you to specify boundary conditions of the form $\vec{n} . (c \nabla u + \alpha u -\gamma) = g-q u$ but there is no ...
7
votes
1answer
176 views

Problem with Neumann condition in quarter disc

So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
4
votes
1answer
124 views

Using NDSolve to solve a system of coupled PDEs

I am trying to solve the Gross-Neveu model in one dimension for a specific soliton initial condition. I am trying ...
1
vote
0answers
72 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times ...
0
votes
0answers
42 views

Boundary condition is not specified on a single edge of the boundary of the computational domain

When I want to solve this PDE I get this error "NDSolve::bcedge: "Boundary condition u[0,0.05]==0 is not specified on a single edge of the boundary of the computational domain"" ...
10
votes
2answers
287 views

How to create subregions for the NDSolve FEM Solver

I am trying to create a 2d region consisting of two subregions. The inner region has several holes, where boundary conditions are applied. The figure shows the idea. I have tried to create this ...
0
votes
0answers
91 views

Using NDSolve to solve a PDE with a Dirac Delta function

I'm trying to solve the following equation (in Mathematica 10): ...
2
votes
0answers
154 views

How to solve a PDE with Robin Boundary Condition inside considered region?

I'm trying to solve the heat diffusion equation in cylindrical coordinates. The main problem is that I would like to include the Robin Boundary Condition inside considered region in order to simulate ...
2
votes
0answers
217 views

How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
1
vote
0answers
62 views

Error when extending 1-dimensional PDE to 2 dimensions

I want to calculate how magnetic flux is trapped in a superconductor near the interface superconductor/vacuum. This problem already was solved analytically by J. Pearl for cylindrical symmetry (if ...
2
votes
2answers
87 views

Extract data from NDSolveValue result

Okay this is a very newbie question. I have coded a sample problem that solves the heat diffusion equation on an annulus. Here's what I have: ...
4
votes
1answer
308 views

PDE with Stefan Conditions, a.k.a variable boundary

I want to solve the one-dimensional one-phase Stefan problem, but I don't know how to make Mathematica understand the conditions. If you are not familiar with what I'm asking please refer to this ...
4
votes
1answer
221 views

Fitting numerical model to experimental data

I have diffusion equation with the initial/boundary conditions: ...
1
vote
0answers
86 views

NDSolve PDE, not enough boundary condition?

The PDE that I want to solve is: $$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ...
1
vote
0answers
90 views

Solving PDEs with complicated boundary conditions

The system I'm trying to solve is $$\nabla^2 C_{(r,\theta)} =0$$ $$C_{(\infty,\theta)}=C_0$$ $$ [ \frac{\partial C_{(r,\theta)}}{\partial r} \cos(\theta)+\frac{1}{r}\frac{\partial ...
1
vote
0answers
113 views

DSolve solve PDE individually but can not solve as a whole PDE system

I have a "simple" system of PDEs, one can be solved easily. But I cant seem to get it work in Mathematica. I am not sure whether I'm having a syntex problem or it's just not doable in Mathematica. ...