Add benchmarks to nonlinear BVPs

benchmarks/NonStiffBVP/nonlinear_wpi.jmd

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+---
+title: Nonlinear BVP Benchmarks
+author: Michelle Zong
+TESTING 
+---
+
+This is a benchmark of MIRK methods and Shooting method on some nonlinear boundary value problems. The testing BVPs are a set of standard BVP test problems as described [here](https://archimede.uniba.it/~bvpsolvers/testsetbvpsolvers/?page_id=29)
+
+# Setup
+
+Fetch required packages.
+
+```julia
+using BoundaryValueDiffEq, OrdinaryDiffEq, DiffEqDevTools, BenchmarkTools, BVProblemLibrary, Weave, Plots
+```
+
+Set up the benchmarked solvers.
+
+```julia
+setups = [ Dict(:alg=>MIRK2(), :dt=>0.1),
+            Dict(:alg=>MIRK3(), :dt=>0.1),
+            Dict(:alg=>MIRK4(), :dt=>0.1),
+            Dict(:alg=>MIRK5(), :dt=>0.1),
+            Dict(:alg=>MIRK6(), :dt=>0.1),]
+labels = ["MIRK2";
+               "MIRK3";
+               "MIRK4";
+               "MIRK5";
+               "MIRK6"];
+```
+
+Sets tolerances.
+
+```julia
+abstols = 1.0 ./ 10.0 .^ (1:4)
+reltols = 1.0 ./ 10.0 .^ (1:4);
+```
+
+# Benchmarks
+
+We here run the BVP benchmarks for all the MIRK methods.
+
+## Nonlinear boundary value problems
+
+### Nonlinear BVP 1
+
+```julia
+prob_1 = BVProblemLibrary.prob_bvp_nonlinear_1
+sol_1 = solve(prob_1, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_1 = TestSolution(sol_1.t, sol_1.u)
+wp_1 = WorkPrecisionSet(prob_1, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_1, 
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_1)
+```
+
+### Nonlinear BVP 2
+
+```julia
+prob_2 = BVProblemLibrary.prob_bvp_nonlinear_2
+sol_2 = solve(prob_2, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_2 = TestSolution(sol_2.t, sol_2.u)
+wp_2 = WorkPrecisionSet(prob_2, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_2,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_2)
+```
+
+### Nonlinear BVP 3
+
+```julia
+prob_3 = BVProblemLibrary.prob_bvp_nonlinear_3
+sol_3 = solve(prob_3, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_3 = TestSolution(sol_3.t, sol_3.u)
+wp_3 = WorkPrecisionSet(prob_3, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_3,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_3)
+```
+
+### Noninear BVP 4
+
+```julia
+prob_4 = BVProblemLibrary.prob_bvp_nonlinear_4
+sol_4 = solve(prob_4, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_4 = TestSolution(sol_4.t, sol_4.u)
+wp_4 = WorkPrecisionSet(prob_4, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_4,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_4)
+```
+
+### Nonlinear BVP 5
+
+```julia
+prob_5 = BVProblemLibrary.prob_bvp_nonlinear_5
+sol_5 = solve(prob_5, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_5 = TestSolution(sol_5.t, sol_5.u)
+wp_5 = WorkPrecisionSet(prob_5, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_5,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_5)
+```
+
+### Nonlinear BVP 6
+
+```julia
+prob_6 = BVProblemLibrary.prob_bvp_nonlinear_6
+sol_6 = solve(prob_6, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_6 = TestSolution(sol_6.t, sol_6.u)
+wp_6 = WorkPrecisionSet(prob_6, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_6,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_6)
+```
+
+### Nonlinear BVP 7
+
+```julia
+prob_7 = BVProblemLibrary.prob_bvp_nonlinear_7
+sol_7 = solve(prob_7, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_7 = TestSolution(sol_7.t, sol_7.u)
+wp_7 = WorkPrecisionSet(prob_7, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_7,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_7)
+```
+
+### Nonlinear BVP 8
+
+```julia
+prob_8 = BVProblemLibrary.prob_bvp_nonlinear_8
+sol_8 = solve(prob_8, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_8 = TestSolution(sol_8.t, sol_8.u)
+wp_8 = WorkPrecisionSet(prob_8, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_8,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_8)
+```
+
+### Nonlinear BVP 9
+
+```julia
+prob_9 = BVProblemLibrary.prob_bvp_nonlinear_9
+sol_9 = solve(prob_9, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_9 = TestSolution(sol_9.t, sol_9.u)
+wp_9 = WorkPrecisionSet(prob_9, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_9,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_9)
+```
+
+### Nonlinear BVP 10
+
+```julia
+prob_10 = BVProblemLibrary.prob_bvp_nonlinear_10
+sol_10 = solve(prob_10, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_10 = TestSolution(sol_10.t, sol_10.u)
+wp_10 = WorkPrecisionSet(prob_10, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_10,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_10)
+```
+
+### Nonlinear BVP 11
+
+```julia
+prob_11 = BVProblemLibrary.prob_bvp_nonlinear_11
+sol_11 = solve(prob_11, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_11 = TestSolution(sol_11.t, sol_11.u)
+wp_11 = WorkPrecisionSet(prob_11, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_11,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_11)
+```
+
+### Nonlinear BVP 12
+
+```julia
+prob_12 = BVProblemLibrary.prob_bvp_nonlinear_12
+sol_12 = solve(prob_12, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_12 = TestSolution(sol_12.t, sol_12.u)
+wp_12 = WorkPrecisionSet(prob_12, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_12,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_12)
+```
+
+### Nonlinear BVP 13
+
+```julia
+prob_13 = BVProblemLibrary.prob_bvp_nonlinear_13
+sol_13 = solve(prob_13, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_13 = TestSolution(sol_13.t, sol_13.u)
+wp_13 = WorkPrecisionSet(prob_13, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_13,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_13)
+```
+
+### Nonlinear BVP 14
+
+```julia
+prob_14 = BVProblemLibrary.prob_bvp_nonlinear_14
+sol_14 = solve(prob_14, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_14 = TestSolution(sol_14.t, sol_14.u)
+wp_14 = WorkPrecisionSet(prob_14, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_14,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000, timeseries_errors=false,verbose=false)
+plot(wp_14)
+```
+
+### Nonlinear BVP 15
+
+```julia
+prob_15 = BVProblemLibrary.prob_bvp_nonlinear_15
+sol_15 = solve(prob_15, MIRK3(), abstol=1e-8, reltol=1e-8, dt = 0.1)
+testsol_15 = TestSolution(sol_15.t, sol_15.u)
+wp_15 = WorkPrecisionSet(prob_15, abstols, reltols, setups; names = labels, print_names = true, appxsol = testsol_15,
+                        dense=false, save_everystep=false,numruns=100,maxiters=10000000,timeseries_errors=false,verbose=false)
+plot(wp_15)
+```
+
+# ```julia, echo = false
+# using SciMLBenchmarks
+# SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])
+# ```