Linked Questions

40
votes
4answers
1k views

Is there a convenient way to copy/paste text-interspersed SE code snippets into Mathematica?

Is there a way to copy and paste code snippets from SE to Mathematica if these snippets are interspersed with text? Like e.g. in Morphing Graphics, color and location in both the question and answer, ...
30
votes
3answers
4k views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ \frac{1}{r}\...
23
votes
2answers
3k views

Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
14
votes
4answers
383 views

Where is the numerical solving breaking down?

I am working with a set of three coupled reaction-diffusion PDEs, and for some parameter values I am getting some not so great solutions. I have been searching documentation and tutorials, and I have ...
8
votes
2answers
748 views

2D inhomogeneous biharmonic equation

How to solve a 2D inhomogeneous biharmonic equation with NDSolve? I tried the following code: ...
13
votes
3answers
896 views

Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)

On this Mathematica.SE form, there exists information on how to use Mathematica to demonstrate the vibration of a circular membrane and the deflection of an orifice plate (the latter I had raised ...
13
votes
2answers
599 views

Conservation of area solving a PDE via finite difference scheme

I have two PDEs that describe the movement of fluid: $h_t + [h^3(1-h)^3((1+\varepsilon h)\sin \theta - \varepsilon h_\theta \cos \theta]_\theta$ = 0 $h_t - [h^3(1-h)^3 \varepsilon h_\theta]_\theta$ = ...
8
votes
3answers
572 views

How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
12
votes
1answer
856 views

Simulating a partial differential equation - reaction-diffusion systems and Turing patterns

I want simulate a reaction-diffusion system described by a PDE called the FitzHugh–Nagumo equation. The system that has been proposed by Alan Turing as a model of animal coat pattern formation and is ...
4
votes
4answers
710 views

Infinite Expression Error NDSolve

I'm trying to figure out why I am consistently getting an infinite expression error when I'm trying to solve this DE using NDSolve. Any help will be appreciated. ...
14
votes
1answer
1k views

Frequency domain Maxwell equations with PML boundary conditions

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
3
votes
2answers
817 views

How to input Robin boundary conditions for nonstandard Laplace equation?

What is the correct way to input these boundary conditions for the following nonstandard Laplace equation, whose coefficients of $\frac{\partial^2 u}{\partial x^2}$ and $\frac{\partial^2 u}{\partial y^...
8
votes
2answers
911 views

How do you find the eigenvalues of a PDE (Dynamic Euler-Bernoulli beam)?

I am continuing to work on the vibration of a beam modeled by the Euler-Bernoulli equation. I have had some good answers to simulating the motion which may be found here. Now I wish to calculate the ...
8
votes
2answers
274 views

Error when solving 't Hooft-Polyakov radial equations using NDSolve

I'm trying to solve 2 coupled nonlinear ODEs using NDSolve, but the solution fails when the parameter $\lambda$ increases. The equations are $$r^2 a''(r)= a(r) [a(r)-1] [a(r)-2]- r^2 [1-a(r)] h(r)^2,$$...
7
votes
2answers
320 views

Solving an unstable BVP numerically, accurately and efficiently

About two weeks ago I've posted the following question on MathOverflow: Solving a boundary value problem numerically, with high precision. That is, the ODE is \begin{equation} y''=y^2-t \tag{1} \end{...

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