diff --git a/tests/test_builtin_solvers.py b/tests/test_builtin_solvers.py
index 37f45b0..88919a7 100644
--- a/tests/test_builtin_solvers.py
+++ b/tests/test_builtin_solvers.py
@@ -46,7 +46,20 @@ def test_instantiate():
             normalized_simulator(num_spatial_dims, num_points)
 
 
-def test_linear_normalized_stepper():
+@pytest.mark.parametrize(
+    "coefficients",
+    [
+        [
+            0.5,
+        ],  # drag
+        [0.0, -0.3],  # advection
+        [0.0, 0.0, 0.01],  # diffusion
+        [0.0, -0.2, 0.01],  # advection-diffusion
+        [0.0, 0.0, 0.0, 0.001],  # dispersion
+        [0.0, 0.0, 0.0, 0.0, -0.0001],  # hyperdiffusion
+    ]
+)
+def test_linear_normalized_stepper(coefficients):
     num_spatial_dims = 1
     domain_extent = 3.0
     num_points = 50
@@ -58,37 +71,27 @@ def test_linear_normalized_stepper():
         cutoff=5,
     )(num_points, key=jax.random.PRNGKey(0))
 
-    for coefficients in (
-        [
-            0.5,
-        ],  # drag
-        [0.0, -0.3],  # advection
-        [0.0, 0.0, 0.01],  # diffusion
-        [0.0, -0.2, 0.01],  # advection-diffusion
-        [0.0, 0.0, 0.0, 0.001],  # dispersion
-        [0.0, 0.0, 0.0, 0.0, -0.0001],  # hyperdiffusion
-    ):
-        regular_linear_stepper = ex.GeneralLinearStepper(
-            num_spatial_dims,
+    regular_linear_stepper = ex.GeneralLinearStepper(
+        num_spatial_dims,
+        domain_extent,
+        num_points,
+        dt,
+        coefficients=coefficients,
+    )
+    normalized_linear_stepper = ex.NormalizedLinearStepper(
+        num_spatial_dims,
+        num_points,
+        normalized_coefficients=ex.normalize_coefficients(
             domain_extent,
-            num_points,
-            dt,
-            coefficients=coefficients,
-        )
-        normalized_linear_stepper = ex.NormalizedLinearStepper(
-            num_spatial_dims,
-            num_points,
-            normalized_coefficients=ex.normalize_coefficients(
-                domain_extent,
-                dt,
-                coefficients,
-            ),
-        )
-
-        regular_linear_pred = regular_linear_stepper(u_0)
-        normalized_linear_pred = normalized_linear_stepper(u_0)
-
-        assert regular_linear_pred == pytest.approx(normalized_linear_pred)
+            coefficients,
+        ),
+        dt=dt,
+    )
+
+    regular_linear_pred = regular_linear_stepper(u_0)
+    normalized_linear_pred = normalized_linear_stepper(u_0)
+
+    assert regular_linear_pred == pytest.approx(normalized_linear_pred, rel=1e-4)
 
 
 def test_nonlinear_normalized_stepper():
@@ -97,7 +100,7 @@ def test_nonlinear_normalized_stepper():
     num_points = 50
     dt = 0.1
     diffusivity = 0.1
-    convection_scale = 0.5
+    convection_scale = 1.0
 
     grid = ex.get_grid(num_spatial_dims, domain_extent, num_points)
     u_0 = jnp.sin(2 * jnp.pi * grid / domain_extent) + 0.3
@@ -116,7 +119,6 @@ def test_nonlinear_normalized_stepper():
         dt=dt,
         normalized_coefficients=ex.normalize_coefficients(
             domain_extent,
-            dt,
             [0.0, 0.0, diffusivity],
         ),
         normalized_convection_scale=ex.normalize_convection_scale(
diff --git a/tests/test_validation.py b/tests/test_validation.py
index e617cb9..d1ae329 100644
--- a/tests/test_validation.py
+++ b/tests/test_validation.py
@@ -46,7 +46,7 @@ def test_diffusion_1d():
     diffusivity = 0.1
 
     analytical_solution = lambda t, x: jnp.exp(
-        -4 * (2 * jnp.pi / domain_extent) ** 2 * diffusivity * t
+        -(4 * 2 * jnp.pi / domain_extent) ** 2 * diffusivity * t
     ) * jnp.sin(4 * 2 * jnp.pi * x / domain_extent)
 
     grid = ex.get_grid(num_spatial_dims, domain_extent, num_points)