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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0
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1answer
67 views

Eigen energies of 2D time independent Schrödinger equation

Firstly, I am aware that a similar question of this type was asked, but it was not helpful as it was only one dimensional (so please don't mark my question as a duplicate) The trouble I am having is ...
0
votes
1answer
70 views

NDSolve::bcedge: Boundary condition not specified on a single edge

NDSolve::bcedge: Boundary condition c[t,5]==Cout is not specified on a single edge of the boundary of the computational domain. >> I'd like to plot $\frac{\partial}{\partial ...
0
votes
0answers
50 views

Stress calculation for stokes equation in 2D

I am solving the Stokes equation for the creeping flow, in a particular geometry, using the stream function formulation. This is my domain: ...
2
votes
1answer
69 views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
3
votes
1answer
90 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
1
vote
0answers
38 views

Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
0
votes
1answer
51 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
6
votes
1answer
59 views

Solving a PDE with a spatially piecewise-constant material parameter

I would like to solve equation for the 2D distribution of an electrical potential in the conductive medium: $$\nabla\cdot(\sigma\nabla f) = 0$$ where $f=f(x,y)$ is the electric potential (in 2D) and ...
1
vote
1answer
82 views

How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0 $$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
3
votes
1answer
165 views

Very slow mathematica finite differences

I have a simple code which solves an equation by an explicit method (FTCS). It takes mathematica several minutes (mathematica 10.0.2) to finish the calculation while the same code in Fortran runs less ...
0
votes
0answers
30 views

NDSolve: basic settings for PDEs

I am trying to learn how to solve PDEs in Mathematica in order to deal with relatively simple problems without needing to formulate weak formulations in FreeFem++, which is rather time consuming for ...
0
votes
1answer
71 views

solving PDE with periodic boundary conditions

I want to solve a 2D-PDE that has the form ...
6
votes
1answer
107 views

DSolve giving strange error messages solving a PDE

Consider this set of PDE $$\left( x^{2}+y^{2}\right) \dfrac {\partial u}{\partial x}+n x y\dfrac{\partial u}{\partial y}=0$$ have general solution $$u\left( x,y\right) =f\left( \dfrac {1}{n-1}\dfrac ...
0
votes
1answer
107 views

Generate a small random disturbance on a flat surface for NDSlove

I want to generate a small random perturbation on a flat surface defined on a square domain, e.g. 1 + 0.05 rand(x,y), which can be used as initial condition with periodic boundary conditions in ...
1
vote
1answer
102 views

PDE solution does not satisfy Neumann boundary conditions using NDSolve

I am trying to solve the free particle Schrodinger equation in 1D (hbar =1, Energy = 1, mass = 1), But specifying conditions only on x==0: ...
0
votes
0answers
84 views

To find a surface with constant Gauss curvature

Please help me use NDSolve to find a surface with constant Gauss curvature $K$ in Cartesian coordinates. I have no previous experience with such differential ...
0
votes
0answers
21 views

Solving an inhomogeneous partial differential equation [duplicate]

Here is my inhomogeneous partial differential equation: $$ \left ( \frac{\partial^2 }{\partial \rho^2}-\frac{1}{\rho} \frac{\partial }{\partial \rho} + \frac{\partial^2 }{\partial z^2}\right ) \psi= ...
0
votes
1answer
57 views

NDSolve`Reinitialize start from previous solution but with different boundary conditions

I am solving a set of coupled partial differential equations (some variation of a 1 dimensional compressible fluid flow). I want to solve the equations (NDSolve, this works fine) but then continue ...
2
votes
2answers
110 views

Overdetermined System of PDEs

EDIT: Just to clarify a large part of my question is whether there is a way to make Mathematica solve a system with more equations than independent variables (so a system that is overdetermined but ...
1
vote
0answers
43 views

Errors when thickness is reduced solving 2D cylindrical heat conduction equation

I am trying to solve the heat conduction equation in cylindrical coordinates with a defined heat generation within the volume (a thin disk, with different heat flux BC top and bottom). The problem is ...
2
votes
1answer
54 views

Solving PDE with Condition on Inside of Region

I'm trying to figure out how to use NDSolve to numerically solve PDEs where some internal values may be specified on the region of the solution. An example, which I picked from a textbook, is solving ...
1
vote
1answer
42 views

How to get the raw data of solutions of partial differential equation in mathematica

I am using NDSolve command of mathematica solving a very complicated partial differential equation (two independents "t" and "x", three master variable "u", "v", "w"). Each time I solve it, it takes ...
6
votes
1answer
131 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 ...
23
votes
3answers
601 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
138 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) ...
15
votes
2answers
230 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
86 views

Dirichlet conditions being ignored

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

Toroidal implicit region looks weird

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

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
5
votes
0answers
120 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 ...
3
votes
1answer
184 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
130 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. ...
10
votes
2answers
600 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
0
votes
0answers
59 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
83 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
219 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
190 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
86 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
213 views

Problem with Neumann condition in quarter disc

Bug persists through version 10.1 So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
4
votes
1answer
174 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
99 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
60 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
383 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
154 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
192 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
317 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
66 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
120 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
383 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
258 views

Fitting numerical model to experimental data

I have diffusion equation with the initial/boundary conditions: ...