@diff_eq

Tweets on ordinary and partial differential equations from @JohnDCook

johndcook.com/blog/partial-differential-equations/
Joined March 2013
  • Tweets4.8K
  • Following17
  • Followers75.9K
297Media
Differential equation modeling johndcook.com/blog/partial-d…
6
20
198
16,587
The Wronskian of two functions is the numerator when using the quotient rule to differentiate their ratio.
13
563
Differential Eqns retweeted
Physics Memes
@ThePhysicsMemes23h
Navier-Stokes is some form of Elvish #calculus
13
169
9
1,389
21,943
Closed-form solutions to nonlinear PDEs johndcook.com/blog/2024/04/2…

Closed-form solutions to nonlinear PDEs

It's uncommon for a differential equation, especially a nonlinear PDE, to have a closed-form solution. But some important nonlinear PDEs can be solved in closed form.

johndcook.com
2
20
2,297
We regard Butcher's work on the classification of numerical integration methods as an impressive example that concrete problem-oriented work can lead to far-reaching conceptual results. -- Alain Connes (Fields medal 1982)
1
18
2,061
Ten life lessons from differential equations johndcook.com/blog/2015/07/2…

Life lessons from differential equations

Some problems simply have no solution. Some problems have no simple solution. Some problems have many solutions. ...

johndcook.com
8
47
3,050
'The more I teach differential equations, the less I understand the mystery of differential equations.' -- Gian-Carlo Rota
5
45
2,709
Eliminating terms from higher order ODEs johndcook.com/blog/2022/11/1…

Eliminating terms from higher-order differential equations

Change of variables to eliminate terms involving (n-1)st derivatives from an nth order differential equation

johndcook.com
20
2,518
Numerical solution of differential-algebraic equations web.mscsoftware.com/support/… (DASSL)
12
2,404
'Classical mathematics concentrated on linear equations for a sound pragmatic reason: it could not solve anything else.' -- Ian Stewart
36
2,505
The differential equation implicit in The Pit and the Pendulum by Edgar Allan Poe. johndcook.com/blog/2026/10/1…
1
6
1,529
2x2 grid giving an overview of numerical differential equation solvers johndcook.com/blog/2020/06/1…

Numerical ODE solver landscape overview

Many methods for solving differential equations numerically can be classified in a 2 x 2 grid: Runge-Kutta or multistep, explicit or implicit.

johndcook.com
1
3
25
2,603
Discretized wave equations terrytao.wordpress.com/2014/…

Discretised wave equations

The wave equation is usually expressed in the form $latex \displaystyle \partial_{tt} u – \Delta u = 0&fg=000000$ where $latex {u \colon {\bf R} \times {\bf R}^d \rightarrow {\bf C}}&…

terrytao.wordpress.com
5
57
6,307
I got an email just now from PDF Expert, an inexpensive alternative to Adobe software. At first glance I thought it said PDE expert, a flashback to an earlier career.
18
2,442
Differential equation on a donut johndcook.com/blog/2025/10/0…

Differential equation on a doughnut

A system of three first-order differential equations whose solutions live on a torus (doughnut).

johndcook.com
1
17
2,890
terrytao.wordpress.com/2014/…

Noether’s theorem, and the conservation laws for the Euler equations

Throughout this post, we will work only at the formal level of analysis, ignoring issues of convergence of integrals, justifying differentiation under the integral sign, and so forth. (Rigorous jus…

terrytao.wordpress.com
4
2
45
4,943
Nonlinear Poisson equation: -Δ u = f(u)
1
1
16
2,484
Noether's theorem, and the conservation laws for the Euler equations
3
2
39
2,922
Difference equations and differential equations johndcook.com/blog/2022/06/1…

Difference equations and differential equations

Example showing how similar the process is for solving difference and differential equations.

johndcook.com
1
14
2,555
History of the finite element method link.springer.com/article/10…

Eighty Years of the Finite Element Method: Birth, Evolution, and Future

Archives of Computational Methods in Engineering - This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis...

link.springer.com
1
5
46
2,735
Wave equation: u_tt - Δu = 0
1
3
1
19
2,630
Load more