diff --git a/examples/tree_1d_dgsem/elixir_advection_PERK2.jl b/examples/tree_1d_dgsem/elixir_advection_PERK2.jl
index dfc95e05907..2dc1c0b0464 100644
--- a/examples/tree_1d_dgsem/elixir_advection_PERK2.jl
+++ b/examples/tree_1d_dgsem/elixir_advection_PERK2.jl
@@ -63,4 +63,3 @@ sol = Trixi.solve(ode, ode_algorithm,
 
 # Print the timer summary
 summary_callback()
-analysis_callback(sol)
\ No newline at end of file
diff --git a/src/callbacks_step/stepsize.jl b/src/callbacks_step/stepsize.jl
index ef7ecc6e5fb..f54bda997b9 100644
--- a/src/callbacks_step/stepsize.jl
+++ b/src/callbacks_step/stepsize.jl
@@ -33,7 +33,7 @@ function Base.show(io::IO, ::MIME"text/plain",
         stepsize_callback = cb.affect!
 
         setup = [
-            "CFL number" => stepsize_callback.cfl_number,
+            "CFL number" => stepsize_callback.cfl_number
         ]
         summary_box(io, "StepsizeCallback", setup)
     end
@@ -64,7 +64,7 @@ end
         t = integrator.t
         u_ode = integrator.u
         semi = integrator.p
-    
+
         # If the integrator is an optimized integrator, calculate cfl number instead of using the input cfl number
         if isa(integrator.alg, PERK2) || isa(integrator.alg, PERK3)
             cfl_number = calculate_cfl_number(u_ode, t, integrator.alg.dt_opt, semi)
@@ -92,11 +92,13 @@ end
 function calculate_cfl_number(u_ode, t, dt_opt, semi::AbstractSemidiscretization)
     mesh, equations, solver, cache = mesh_equations_solver_cache(semi)
     u = wrap_array(u_ode, mesh, equations, solver, cache)
-    max_dt_variable = max_dt(u, t, mesh,have_constant_speed(equations), equations, solver, cache)
+    max_dt_variable = max_dt(u, t, mesh, have_constant_speed(equations), equations,
+                             solver, cache)
+    # For debugging purpose, especially for PERK3
     println("max_dt $max_dt_variable")
     cfl_number = dt_opt / max_dt(u, t, mesh,
-                 have_constant_speed(equations), equations,
-                 solver, cache)
+                        have_constant_speed(equations), equations,
+                        solver, cache)
 
     return cfl_number
 end
diff --git a/src/time_integration/paired_explicit_runge_kutta/methods_PERK2.jl b/src/time_integration/paired_explicit_runge_kutta/methods_PERK2.jl
index a603e7270bf..7049b4a6d70 100644
--- a/src/time_integration/paired_explicit_runge_kutta/methods_PERK2.jl
+++ b/src/time_integration/paired_explicit_runge_kutta/methods_PERK2.jl
@@ -138,8 +138,10 @@ mutable struct PERK2 <: PERKSingle
         newPERK2 = new(num_stages)
 
         newPERK2.a_matrix, newPERK2.c, newPERK2.dt_opt = compute_PERK2_butcher_tableau(num_stages,
-                                                                      eig_vals, tspan,
-                                                                      bS, c_end)
+                                                                                       eig_vals,
+                                                                                       tspan,
+                                                                                       bS,
+                                                                                       c_end)
 
         newPERK2.b1 = one(bS) - bS
         newPERK2.bS = bS
@@ -153,8 +155,10 @@ mutable struct PERK2 <: PERKSingle
         newPERK2 = new(num_stages)
 
         newPERK2.a_matrix, newPERK2.c, newPERK2.dt_opt = compute_PERK2_butcher_tableau(num_stages,
-                                                                      eig_vals, tspan,
-                                                                      bS, c_end)
+                                                                                       eig_vals,
+                                                                                       tspan,
+                                                                                       bS,
+                                                                                       c_end)
 
         newPERK2.b1 = one(bS) - bS
         newPERK2.bS = bS
@@ -288,7 +292,7 @@ function solve!(integrator::PERK2Integrator)
             end
 
             # Higher stages
-            for stage in 3:alg.num_stages
+            for stage in 3:(alg.num_stages)
                 # Construct current state
                 @threaded for i in eachindex(integrator.du)
                     integrator.u_tmp[i] = integrator.u[i] +
diff --git a/src/time_integration/paired_explicit_runge_kutta/methods_PERK3.jl b/src/time_integration/paired_explicit_runge_kutta/methods_PERK3.jl
index ea66d2ce356..cf9bc7d233d 100644
--- a/src/time_integration/paired_explicit_runge_kutta/methods_PERK3.jl
+++ b/src/time_integration/paired_explicit_runge_kutta/methods_PERK3.jl
@@ -196,9 +196,10 @@ mutable struct PERK3 <: PERKSingle
         eig_vals = eigvals(jacobian_ad_forward(semi))
         newPERK3 = new(num_stages)
 
-        newPERK3.a_matrix, newPERK3.c, newPERK3.dt_opt = compute_PERK3_Butcher_tableau(num_stages, tspan,
-                                                                      eig_vals,
-                                                                      c_s2)
+        newPERK3.a_matrix, newPERK3.c, newPERK3.dt_opt = compute_PERK3_Butcher_tableau(num_stages,
+                                                                                       tspan,
+                                                                                       eig_vals,
+                                                                                       c_s2)
 
         return newPERK3
     end
@@ -208,9 +209,10 @@ mutable struct PERK3 <: PERKSingle
                    c_s2 = 1.0)
         newPERK3 = new(num_stages)
 
-        newPERK3.a_matrix, newPERK3.c, newPERK3.dt_opt = compute_PERK3_Butcher_tableau(num_stages, tspan,
-                                                                      eig_vals,
-                                                                      c_s2)
+        newPERK3.a_matrix, newPERK3.c, newPERK3.dt_opt = compute_PERK3_Butcher_tableau(num_stages,
+                                                                                       tspan,
+                                                                                       eig_vals,
+                                                                                       c_s2)
         return newPERK3
     end
 end # struct PERK3