@diff_eq

Tweets on ordinary and partial differential equations from @JohnDCook

johndcook.com/blog/partial-differential-equations/
Joined March 2013
  • Tweets4.7K
  • Following17
  • Followers75.9K
297Media
Include

Only show posts containing:

Exclude

Hide posts containing:

Time range
-
Minimum likes
'The more I teach differential equations, the less I understand the mystery of differential equations.' -- Gian-Carlo Rota
2
34
2,009
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
2,483
Numerical solution of differential-algebraic equations web.mscsoftware.com/support/… (DASSL)
12
2,371
'Classical mathematics concentrated on linear equations for a sound pragmatic reason: it could not solve anything else.' -- Ian Stewart
36
2,490
The differential equation implicit in The Pit and the Pendulum by Edgar Allan Poe. johndcook.com/blog/2026/10/1…
1
6
1,510
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
26
2,590
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
6,276
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.
19
2,434
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
2,885
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
4,934
Nonlinear Poisson equation: -Δ u = f(u)
1
1
16
2,482
Noether's theorem, and the conservation laws for the Euler equations
3
2
37
2,920
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
2,552
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
2,731
Wave equation: u_tt - Δu = 0
1
3
1
19
2,627
'The history of transistors is the history of solving Schrödinger's equation in various materials.' -- Leon Lederman
10
65
3,347
Operator calculus johndcook.com/blog/2022/10/1…

Operational calculus for solving differential equations

A justification for useful tricks that seem unjustified, and a worked-out example

johndcook.com
1
29
2,602
Scalar reaction-diffusion equation: u_t - Δu = f(u)
16
2,670
Solving the wave equation on a disk johndcook.com/blog/2021/06/1…

Solving the wave equation on a disk

Modeling a vibrating circular membrane, like a drum head, using the wave equation in polar coordinates.

johndcook.com
5
25
2,470
Lorenz Attractor animation lkforge.com/tools/physics/lo…

Lorenz Attractor — Interactive 3D Strange Attractor | LK Forge

Spin the 3D butterfly, turn the ρ dial, and split a twin trajectory to watch the butterfly effect diverge on a log plot. Free, no sign-up, embeddable.

lkforge.com
1
17
2,515
Load more