Open AshtonSBradley opened 3 months ago
Describe the example
Predator-prey solution is wrong using defaults. Also occurs if we instead use defaults in DifferentialEquations.
Doesn't seem to occur if we switch to e.g. Vern6 defaults.
Minimal Reproducible Example 👇
using OrdinaryDiffEq using Plots # system parameters λ = .7 # 🐇 linear growth - bunnies reproduce γ = 0.4 # 🐇 nonlinear loss - wolf eats rabbit κ = 0.3 # 🐺 nonlinear growth - wolf eats rabbit β = 1.2 # 🐺 linear loss - wolves get old p = [λ γ β κ] function pprey(u,p,t) λ,γ,β,κ = p r,w = u dr = λ*r - γ*r*w dw = - β*w + κ*r*w return [dr;dw] end r̄, w̄ = β/κ, λ/γ ti = 0.0 tf = 50.0 Nt = 200 t = LinRange(ti,tf,Nt) alg = Tsit5() # alg = Vern6() # Much better default u0 = [β/κ + .2 ; λ/γ] # lots of carrots this month! prob = ODEProblem(pprey,u0,(ti,tf),p) sol = solve(prob,alg=Tsit5(),saveat=t); # default reltol=1e-3 (??!!) # sol = solve(prob,alg=Tsit5(),saveat=t,reltol=1e-4); sol2 = solve(prob,alg=Vern6(),saveat=t); r = sol[1,:]; w = sol[2,:]; r2= sol2[1,:]; w2 = sol2[2,:]; plot(r,w,size=(450,300),label="numerical solution") plot!(r2,w2,label="correct numerical") scatter!([r̄],[w̄],label="steady state",legend=:outerright) xlabel!("rabbits") ylabel!("wolves")
Not Working Environment (please complete the following information):
using Pkg; Pkg.status()
julia> Pkg.status() Status `~/Dropbox/Teaching/2024/phsi365/integrator_test/Project.toml` ⌃ [1dea7af3] OrdinaryDiffEq v6.49.4 [91a5bcdd] Plots v1.40.2
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
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versioninfo()
Julia Version 1.10.2 Commit bd47eca2c8a (2024-03-01 10:14 UTC) Build Info: Official https://julialang.org/ release Platform Info: OS: macOS (x86_64-apple-darwin22.4.0) CPU: 16 × Intel(R) Core(TM) i9-9900K CPU @ 3.60GHz WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, skylake) Threads: 8 default, 0 interactive, 4 GC (on 16 virtual cores) Environment: JULIA_NUM_THREADS = 8 JULIA_PKG_DEVDIR = /Users/abradley/Dropbox/Julia/Dev JULIA_EDITOR = code
Additional context
Here it is clear that this isn't the solution, which should be periodic, and is found by a small reduction in tolerance to e.g. reltol=1e-4. Alternately, switching to alg=Vern6() with default tolerances produces a credible solution.
reltol=1e-4
Describe the example
Predator-prey solution is wrong using defaults. Also occurs if we instead use defaults in DifferentialEquations.
Doesn't seem to occur if we switch to e.g. Vern6 defaults.
Minimal Reproducible Example 👇
Not Working Environment (please complete the following information):
using Pkg; Pkg.status()using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)versioninfo()Additional context
Here it is clear that this isn't the solution, which should be periodic, and is found by a small reduction in tolerance to e.g.
reltol=1e-4. Alternately, switching to alg=Vern6() with default tolerances produces a credible solution.