Add silence_sundials_errors solver option (#5290)

* feat: add`silence_sundial_warnings` solver option

* refactor: `silence_sundials_warnings` -> `silence_sundials_errors`

Author: BradyPlanden

CHANGELOG.md

@@ -2,6 +2,8 @@
 
 ## Features
 
+- Adds `silence_sundials_errors` IDAKLU solver option with `default=False` to match historical output. ([#5290](https://github.com/pybamm-team/PyBaMM/pull/5290))
+
 ## Bug fixes
 
 # [v25.10.2](https://github.com/pybamm-team/PyBaMM/tree/v25.10.2) - 2025-11-27

src/pybamm/solvers/idaklu_solver.py

@@ -76,6 +76,8 @@ class IDAKLUSolver(pybamm.BaseSolver):
                 "increment_factor": 1.0,
                 # Enable or disable linear solution scaling
                 "linear_solution_scaling": True,
+                # Silence Sundials errors during solve
+                "silence_sundials_errors": False,
                 ## Main solver
                 # Maximum order of the linear multistep method
                 "max_order_bdf": 5,
@@ -176,6 +178,7 @@ def __init__(
             "epsilon_linear_tolerance": 0.05,
             "increment_factor": 1.0,
             "linear_solution_scaling": True,
+            "silence_sundials_errors": False,
             "max_order_bdf": 5,
             "max_num_steps": 100000,
             "dt_init": 0.0,