Improve tests for ODE integrators and fix typos in tableaus
Created by: femtobit
Prompted by #1056 (closed), this PR
- fixes the typo in the RK4 tableau reported in the issue linked above. The typo was on the diagonal of the
a
matrix of the RK tableau.a
is supposed to be a strictly lower triangular matrix and only those parts affect the result oftableau.step
, so the typo did not cause any error in the actual results computed by the solver. - improves the tests for fixed-step ODE solvers to be more sensitive to errors in the tableaus. In particular, the previous tests are insensitive to errors in
tableau.a
, even those in the lower triangle which would affect results if present. - adds a test case
test_tableau
which does some sanity checks on the tableaus themselves (such as assertinga
is strictly lower triangular). - Fixes a typo in
bt_feuler
, which is fixed-step but did have a 2-dimensionalb
. This also should not have affected results, but is conceptually incorrect.