Adds additional tests for Casadi modes (#4028)

* Add casadi solver mode tests

* add experiment definition to test

* tests: relocate to integration, update for pytest.

---------

Co-authored-by: Martin Robinson <martinjrobins@gmail.com>

tests/integration/test_solvers/test_casadi_mode.py

@@ -0,0 +1,56 @@
+#
+# Tests for the Casadi Solver Modes
+#
+
+import pybamm
+import numpy as np
+
+
+class TestCasadiModes:
+    def test_casadi_solver_mode(self):
+        solvers = [
+            pybamm.CasadiSolver(mode="safe", atol=1e-6, rtol=1e-6),
+            pybamm.CasadiSolver(mode="fast", atol=1e-6, rtol=1e-6),
+            pybamm.CasadiSolver(mode="fast with events", atol=1e-6, rtol=1e-6),
+        ]
+
+        # define experiment
+        experiment = pybamm.Experiment(
+            [
+                ("Discharge at 1C until 3.0 V (10 seconds period)",),
+            ]
+        )
+
+        solutions = []
+        for solver in solvers:
+            # define model
+            model = pybamm.lithium_ion.SPM()
+
+            # solve simulation
+            sim = pybamm.Simulation(
+                model,
+                experiment=experiment,
+                solver=solver,
+            )
+
+            # append to solutions
+            solutions.append(sim.solve())
+
+        # define variables to compare
+        output_vars = [
+            "Terminal voltage [V]",
+            "Positive particle surface concentration [mol.m-3]",
+            "Electrolyte concentration [mol.m-3]",
+        ]
+
+        # assert solutions
+        for var in output_vars:
+            np.testing.assert_allclose(
+                solutions[0][var].data, solutions[1][var].data, rtol=1e-6, atol=1e-6
+            )
+            np.testing.assert_allclose(
+                solutions[0][var].data, solutions[2][var].data, rtol=1e-6, atol=1e-6
+            )
+            np.testing.assert_allclose(
+                solutions[1][var].data, solutions[2][var].data, rtol=1e-6, atol=1e-6
+            )