Serial (rank-aware-decomp-agnostic) Newton + banded-solve body for backward Euler. Operates entirely on state%ub / state%resid; the caller is responsible for sizing the state correctly. Does NOT call compute_resid_glob — the wrapper does, after restore_local_layout brings every rank back to its local view so the par_sum_real call involves all ranks.
Backward Euler is the (c_resid, c1, c2) = (1, 1, 0) degenerate case of the shared run_newton BDF solve, so it simply delegates.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| type(solver_state_t), | intent(inout) | :: | state |