# Questions tagged [differential-equations]

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

6,242 questions
Filter by
Sorted by
Tagged with
4answers
9k views

### Lyapunov Exponent

Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System? Thank you Rossler System: ...
4answers
2k views

### Only final result from NDSolve

Finally, I started to play with differential equations in Mathematica. And I have faced the problem, which seems to me so basic that I'm afraid this question is going to be closed soon. However, I'...
2answers
6k views

3answers
6k views

### How to discretize a nonlinear PDE fast?

I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
2answers
7k views

### Elegant way of obtaining the envelope of oscillating function [duplicate]

I am solving a differential equation numerically and the output is an oscillating function with the amplitude of the oscillation decaying in time. I would like to extract the power law governing this ...
2answers
1k views

1answer
369 views

### Stable fluids code for electromagnetic mixture application

This code has been translated from the original Jos Stam code and improved with some Mathematica functions. It solves problem of viscous incompressible flow with electromagnetic force in a rectangle ...
1answer
5k views

### What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
1answer
706 views

### Solver for COVID-19 epidemic model with the Caputo fractional derivatives

As it is known in biological system with memory it would be suitable to use fractional derivatives to describe evolution of the system. In a current version of Mathematica 12.1 there is no special ...
2answers
1k views

### What boundary is added when boundary condition is not sufficient?

When insufficient boundary conditions are given to NDSolve for solving PDE, usually the warning NDSolve::bcart pops up: ...
4answers
3k views

### Plot MATLAB icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here and here, but I can't understand it very well. (I admit that, though playing with ...
4answers
902 views

### How to model diffusion through a membrane?

This is a follow-up on How to handle discontinuity in diffusion coefficient? Consider diffusion of $u(t,x)$ on the domain $x \in [0,2]$ with some simple boundary conditions such as \$u(0) = 2, u(2) = ...