Largest PDE ever?

[SLD]

Just curious is there a world record PDE solved? That is a maximum number of variables? Can our best super computer solve a 20 variable PDE, I would assume any such solution would need to be numerically solved. How about 1,000 variables?

 

[Bomb#20]

Just curious is there a world record PDE solved? That is a maximum number of variables? Can our best super computer solve a 20 variable PDE, I would assume any such solution would need to be numerically solved. How about 1,000 variables?

Probably depends on how you define "solve". But as of 2004, using god knows how many special ad hoc tricks and approximations, state of the art for solving the Schroedinger equation numerically to an accuracy of a couple percent was 67 million variables.

https://physicstoday.scitation.org/doi/10.1063/1.1688069

 

[steve_bank]

https://pdesolutions.com/

Lok here they have a demo version with example.

I was aware of digita control systems with upwards of a hundred variables.

The general technique these days is Finite Element Analysis for physical problems like electromagnetic and heat transfer. That is what the link uses.

In linear systems it is State Space or Stace Variables. It is all matrix solutions of dynamic equations.