Add new stiff ODE benchmark problems

benchmarks/StiffODE/E5.jmd

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+---
+title: E5 Work-Precision Diagrams
+author: Chris Rackauckas
+---
+
+```julia
+using OrdinaryDiffEq, DiffEqDevTools, Sundials, Plots, ODEInterfaceDiffEq, LSODA
+using LinearAlgebra, StaticArrays, RecursiveFactorization
+using OrdinaryDiffEqFIRK
+gr()
+
+# E5 Problem from Stiff Test Set
+# Exact implementation based on the Fortran feval subroutine
+# 4-dimensional stiff ODE system with widely separated rate constants
+
+function e5!(du, u, p, t)
+    # E5 problem - exact translation from Fortran feval subroutine:
+    # prod1=7.89D-10*y(1)
+    # prod2=1.1D7*y(1)*y(3)  
+    # prod3=1.13D9*y(2)*y(3)
+    # prod4=1.13D3*y(4)
+    # f(1)=-prod1-prod2
+    # f(2)=prod1-prod3
+    # f(4)=prod2-prod4
+    # f(3)=f(2)-f(4)
+
+    prod1 = 7.89e-10 * u[1]
+    prod2 = 1.1e7 * u[1] * u[3]
+    prod3 = 1.13e9 * u[2] * u[3]
+    prod4 = 1.13e3 * u[4]
+
+    du[1] = -prod1 - prod2        # f(1)
+    du[2] = prod1 - prod3         # f(2) 
+    du[4] = prod2 - prod4         # f(4)
+    du[3] = du[2] - du[4]         # f(3) = f(2) - f(4)
+end
+
+function e5(u, p, t)
+    # E5 problem - exact translation from Fortran feval subroutine:
+    # prod1=7.89D-10*y(1)
+    # prod2=1.1D7*y(1)*y(3)  
+    # prod3=1.13D9*y(2)*y(3)
+    # prod4=1.13D3*y(4)
+    # f(1)=-prod1-prod2
+    # f(2)=prod1-prod3
+    # f(4)=prod2-prod4
+    # f(3)=f(2)-f(4)
+
+    prod1 = 7.89e-10 * u[1]
+    prod2 = 1.1e7 * u[1] * u[3]
+    prod3 = 1.13e9 * u[2] * u[3]
+    prod4 = 1.13e3 * u[4]
+
+    du1 = -prod1 - prod2        # f(1)
+    du2 = prod1 - prod3         # f(2) 
+    du4 = prod2 - prod4         # f(4)
+    du3 = du2 - du4         # f(3) = f(2) - f(4)
+    SA[du1,du2,du3,du4]
+end
+
+# Initial conditions - system starts with all mass in species A
+u0 = [1.76e-3, 0.0, 0.0, 0.0]
+
+# Time span - long enough to see both fast and slow time scales
+tspan = (0.0, 1e10)
+
+prob = ODEProblem{true, SciMLBase.FullSpecialize}(e5!, u0, tspan)
+probstatic = ODEProblem{false}(e5, SVector{4}(u0), tspan)
+probbig = ODEProblem{true, SciMLBase.FullSpecialize}(e5!, big.(u0), big.(tspan))
+
+# Generate reference solution
+sol = solve(probbig, Rodas5P(), abstol=1/10^60, reltol=1/10^30)
+probs = [prob, probstatic]
+test_sol = [sol, sol]
+
+abstols = [1.7e-28 for i in 1:2]
+reltols = 10.0 .^ -(6 .+ (1:2)./4)
+```
+
+```julia
+ylabels = 10.0 .^ (-30:2:0)
+plot(sol, xscale=:log10, yscale=:log10, tspan = (1e-5, 1e10), labels=["A" "B" "C" "D"], yticks = ylabels)
+```
+
+## Benchmarks
+
+```julia
+setups = [Dict(:alg=>Rosenbrock23()),
+          Dict(:alg=>Rosenbrock23(), :prob_choice => 2),
+          Dict(:alg=>lsoda()),
+        Dict(:alg=>Rodas5P()),
+          Dict(:alg=>Rodas5P(), :prob_choice => 2),
+          Dict(:alg=>FBDF()),
+          Dict(:alg=>QNDF()),
+          Dict(:alg=>TRBDF2()),
+          Dict(:alg=>CVODE_BDF()),
+          #Dict(:alg=>rodas()),
+          #Dict(:alg=>radau()),
+          Dict(:alg=>RadauIIA5()),
+          Dict(:alg=>ROS34PW1a()),
+
+          ]
+wp = WorkPrecisionSet(probs,abstols,reltols,setups; error_estimate = :l2, verbose=false, dense=false,
+                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=10)
+plot(wp)
+```
+
+```julia
+setups = [Dict(:alg=>FBDF()),
+          Dict(:alg=>QNDF()),
+          Dict(:alg=>CVODE_BDF()),
+          Dict(:alg=>lsoda()),
+          Dict(:alg=>ddebdf()),
+          Dict(:alg=>Rodas5P()),
+          Dict(:alg=>Rodas5P(), :prob_choice => 2),
+          Dict(:alg=>rodas()), 
+          Dict(:alg=>radau()),
+          Dict(:alg=>RadauIIA5()),
+]
+wp = WorkPrecisionSet(probs,abstols,reltols,setups; verbose=false, dense=false,
+                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=10)
+plot(wp)
+```
+
+```julia
+setups = [Dict(:alg=>Kvaerno4()),
+          Dict(:alg=>Kvaerno5()),
+          Dict(:alg=>CVODE_BDF()),
+          Dict(:alg=>KenCarp4()),
+          Dict(:alg=>KenCarp47()),
+          Dict(:alg=>KenCarp47(), :prob_choice => 2),
+          Dict(:alg=>KenCarp5()),
+          Dict(:alg=>lsoda()),
+          Dict(:alg=>Rodas5P()),
+          Dict(:alg=>Rodas5P(), :prob_choice => 2),
+        Dict(:alg=>ImplicitEulerExtrapolation(min_order = 4, init_order = 11,threading = OrdinaryDiffEq.PolyesterThreads())),
+        Dict(:alg=>ImplicitEulerExtrapolation(min_order = 4, init_order = 11,threading = false)),
+        Dict(:alg=>ImplicitEulerBarycentricExtrapolation(min_order = 4, init_order = 11, threading = OrdinaryDiffEq.PolyesterThreads())),
+        Dict(:alg=>ImplicitEulerBarycentricExtrapolation(min_order = 4, init_order = 11, threading = false)),
+        Dict(:alg=>ImplicitHairerWannerExtrapolation(min_order = 3, init_order = 111,threading = OrdinaryDiffEq.PolyesterThreads())),
+        Dict(:alg=>ImplicitHairerWannerExtrapolation(min_order = 3, init_order = 11,threading = false)),
+          ]
+wp = WorkPrecisionSet(probs,abstols,reltols,setups; verbose=false, dense=false,
+                      save_everystep=false,appxsol=test_sol,maxiters=Int(1e5),numruns=10)
+plot(wp)
+```
+
+```julia, echo = false
+using SciMLBenchmarks
+SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])
+```