Linear 100x100 Work-Precision Diagrams (including ESERK4)

For these tests we will solve an 100x100 system of linear differential equations. This will demonstrate the efficiency of the methods for handling large systems.

Problem

using Pkg
Pkg.update()
using OrdinaryDiffEq, DiffEqDevTools, Plots, Random
Random.seed!(123)
gr()

# 2D Linear ODE
function f(du,u,p,t)
  @inbounds for i in eachindex(u)
    du[i] = 1.01*u[i]
  end
end
function f_analytic(u₀,p,t)
  u₀*exp(1.01*t)
end
tspan = (0.0,10.0)
prob = ODEProblem(ODEFunction(f,analytic=f_analytic),rand(100,100),tspan)

abstols = 1.0 ./ 10.0 .^ (6:13)
reltols = 1.0 ./ 10.0 .^ (3:10);

429.4s

Julia

Setup

setups = [
          Dict(:alg=>DP5()),
          Dict(:alg=>BS5()),
          Dict(:alg=>Tsit5()),
          Dict(:alg=>Vern6()),
          #Dict(:alg=>RKC()),
          Dict(:alg=>ROCK2()),
          Dict(:alg=>ROCK4()),
          Dict(:alg=>SERK2(controller=:PI)),
          Dict(:alg=>SERK2(controller=:Predictive)),
  				Dict(:alg=>ESERK4()),
          Dict(:alg=>ESERK5())
          ]
#Names = ["DP5" "BS5" "Tsit5" "Vern6" "RKC" "ROCK2" "ROCK4" "SERK2 PI" "SERK2 Predictive" "ESERK5"]
Names = ["DP5" "BS5" "Tsit5" "Vern6" "ROCK2" "ROCK4" "SERK2 PI" "SERK2 Predictive" "ESERK4" "ESERK5"]

3.6s

Julia

1×10 Array{String,2}: "DP5" "BS5" "Tsit5" "Vern6" "ROCK2" "ROCK4" … "ESERK4" "ESERK5"

Speed Only Tests

wp = WorkPrecisionSet(prob,abstols,reltols,setups;names=Names,save_everystep=false,numruns=5,maxiters=Int(1e8))
plot(wp,dpi=200,linewidth=1,legend=:topright,legendfontsize=6)

2830.7s

Julia

We are getting reasonable performance. RKC could not solve with the given iterations.