Linked Questions

82
votes
16answers
4k views

Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 all fundamental FEM solvers (linear, nonlinear, stationary, ...
1
vote
2answers
121 views

Heat balance in layer coupled via BC

I am trying to solve the heat balance in a 3 layer system in Mathematica 12.0.0. Each layer has different thermal properties. The layers are coupled via the boundary conditions (Neumann type) to ...
57
votes
1answer
5k views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
2
votes
1answer
148 views

Neumann boundary condition ignored

Im trying to solve a system of two PDE (im[t,x] and ia[t,x]) that are dependent on time and distance. I’m using my own anisotropic mesh (thanks to @TimLaska) that is aimed to represent an interface ...
4
votes
2answers
281 views

1D mesh generation for PDE solution

I'm trying to solve a system of two PDE that are dependent on time and distance (H[x,t] and P[x,t]). I'm solving the problem using the method of lines but I want to generate myself the mesh and ...
5
votes
2answers
382 views

NDSolve with equation system with unknown functions defined on different domains

Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below: Equations: ...
4
votes
1answer
134 views

Trouble with dependent variables in NDSolve while modelling transparent boundary conditions on a quantum graph with Mathematica

I am trying to create a model of plane wave's propagation on a quantum graph(metric graph with a differential operator, Shrodinger operator in my case, along the edges and continuity condition at the ...
9
votes
1answer
327 views

How to handle discontinuity in diffusion coefficient?

I am looking to solve the diffusion equation with a discontinuous jump in the diffusion coefficient. In 1D, the diffusion equation for $u(t,x)$ is: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
19
votes
4answers
978 views

How to apply different equations to different parts of a geometry in PDE?

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
4
votes
3answers
623 views

Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...