fix docs for time_dependent tutorial (#271)

Author: oameye

docs/src/tutorials/limit_cycles.md

@@ -109,7 +109,7 @@ sweep = ParameterSweep(F0 => (0.002, 0.011), (0,T))
 
 # start from initial_state, use sweep, total time is 2*T
 time_problem = ODEProblem(harmonic_eq, initial_state, sweep=sweep, timespan=(0,2*T))
-time_evo = solve(time_problem, saveat=100);
+time_evo = solve(time_problem, Tsit5(), saveat=100);
 nothing # hide
 ```
 Inspecting the amplitude as a function of time,

docs/src/tutorials/time_dependent.md

@@ -42,7 +42,7 @@ Given $\mathbf{u}(T_0)$, what is $\mathbf{u}(T)$ at future times?
 
 For constant parameters, a [`HarmonicEquation`](@ref HarmonicBalance.HarmonicEquation) object can be fed into the constructor of [`ODEProblem`](@ref ODEProblem). The syntax is similar to DifferentialEquations.jl :
 ```@example time_dependent
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 x0 = [0.; 0.] # initial condition
 fixed = (ω0 => 1.0, γ => 1e-2, λ => 5e-2, F => 1e-3,  α => 1.0, η => 0.3, θ => 0, ω => 1.0) # parameter values
 
@@ -51,15 +51,15 @@ ode_problem = ODEProblem(harmonic_eq, fixed, x0 = x0, timespan = (0,1000))
 OrdinaryDiffEq.jl takes it from here - we only need to use `solve`.
 
 ```@example time_dependent
-time_evo = solve(ode_problem, saveat=1.0);
+time_evo = solve(ode_problem, Tsit5(), saveat=1.0);
 plot(time_evo, ["u1", "v1"], harmonic_eq)
 ```
 
 Running the above code with `x0 = [0.2, 0.2]` gives the plots
 ```@example time_dependent
 x0 = [0.2; 0.2] # initial condition
 ode_problem = remake(ode_problem, u0 = x0)
-time_evo = solve(ode_problem, saveat=1.0);
+time_evo = solve(ode_problem, Tsit5(), saveat=1.0);
 plot(time_evo, ["u1", "v1"], harmonic_eq)
 ```
 
@@ -85,7 +85,7 @@ The sweep linearly interpolates between $\omega = 0.9$ at time 0 and $\omega  =
 Let us now define a new `ODEProblem` which incorporates `sweep` and again use `solve`:
 ```@example time_dependent
 ode_problem = ODEProblem(harmonic_eq, fixed, sweep=sweep, x0=[0.1;0.0], timespan=(0, 2e4))
-time_evo = solve(ode_problem, saveat=100)
+time_evo = solve(ode_problem, Tsit5(), saveat=100)
 plot(time_evo, "sqrt(u1^2 + v1^2)", harmonic_eq)
 ```
 We see the system first evolves from the initial condition towards the low-amplitude steady state. The amplitude increases as the sweep proceeds, with a jump occurring around $\omega = 1.08$ (i.e., time 18000).