Add more tests

Author: tansongchen

bench/non_stiff.jl

@@ -12,9 +12,35 @@ function lotka(du, u, p, t)
     du[1] = p[1] * x - p[2] * x * y
     du[2] = -p[3] * y + p[4] * x * y
 end
-prob = ODEProblem{true, SciMLBase.FullSpecialize}(
+prob_lotka = ODEProblem{true, SciMLBase.FullSpecialize}(
     lotka, [1.0, 1.0], (0.0, 10.0), [1.5, 1.0, 3.0, 1.0])
-sol = solve(prob, Vern7(), abstol = 1 / 10^14, reltol = 1 / 10^14)
+sol_lotka = solve(prob_lotka, Vern7(), abstol = 1e-14, reltol = 1e-14)
+
+function fitzhugh(du, u, p, t)
+    v = u[1]
+    w = u[2]
+    a = p[1]
+    b = p[2]
+    τinv = p[3]
+    l = p[4]
+    du[1] = v - v^3 / 3 - w + l
+    du[2] = τinv * (v + a - b * w)
+end
+prob_fitzhugh = ODEProblem{true, SciMLBase.FullSpecialize}(
+    fitzhugh, [1.0; 1.0], (0.0, 10.0), [0.7, 0.8, 1 / 12.5, 0.5])
+sol_fitzhugh = solve(prob_fitzhugh, Vern7(), abstol = 1e-14, reltol = 1e-14)
+
+function rigid(du, u, p, t)
+    I₁ = p[1]
+    I₂ = p[2]
+    I₃ = p[3]
+    du[1] = I₁ * u[2] * u[3]
+    du[2] = I₂ * u[1] * u[3]
+    du[3] = I₃ * u[1] * u[2] + 0.25 * sin(t)^2
+end
+prob_rigid = ODEProblem{true, SciMLBase.FullSpecialize}(
+    rigid, [1.0; 0.0; 0.9], (0.0, 10.0), [-2.0, 1.25, -0.5])
+sol_rigid = solve(prob_rigid, Vern7(), abstol = 1e-14, reltol = 1e-14);
 
 # Make work-precision plot
 setups = [Dict(:alg => DP5())
@@ -26,6 +52,13 @@ for order in 6:2:12
     push!(names, "Taylor $(order)")
     push!(setups, Dict(:alg => ExplicitTaylor(order = Val(order + 1))))
 end
-wp = WorkPrecisionSet([prob], abstols, reltols, setups; names = names, appxsol = [sol],
-    save_everystep = false, numruns = 100, maxiters = 10000)
-plot(wp)
+
+function make_plot(prob, sol)
+    wp = WorkPrecisionSet([prob], abstols, reltols, setups; names = names, appxsol = [sol],
+        save_everystep = false, numruns = 100, maxiters = 10000)
+    p = plot(wp)
+    return p
+end
+p_lotka = make_plot(prob_lotka, sol_lotka)
+p_fitzhugh = make_plot(prob_fitzhugh, sol_fitzhugh)
+p_rigid = make_plot(prob_rigid, sol_rigid)