Progress

Conjecture: There does not exist A-stable (DIRK/IRK) methods with positive coefficients and of order 3 or higher

In this repository, we already have Mathematica scripts for testing the conjecture for IRK/DIRK methods of order 3, with 2 and 3 stages. The way we impose A-stability is by requiring the invariants of the matrix M to be nonnegative.

This works for 2-stage where Mathematica outputs “false” confirming there is no solution. For 3 stage method, Mathematica executes forever.

We can discuss this with ‪Lajos this week

Feb 14

• Shared overleaf document containing the progress so far with Lajos, David, and Abhijit

Feb 22nd

• Yousef needs to specify the specific order condition which if removed, mathematica can produce a solution/or confirmation that there is no solution.

• Yousef noticed some discrepancies between his old notes and when trying mathematica today. Need to confirm them and share this in the overleaf doc.