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ODE Solvers

This package solves the GC migration and peak-width ODEs through OrdinaryDiffEq.jl. The solver is selected via Options(alg=...). Common solvers are re-exported from GasChromatographySimulator, so they can be used without importing OrdinaryDiffEq directly.

  • OwrenZen5() (default): Good accuracy and stability for GC simulations.
  • Tsit5(): Modern, efficient 5th-order method. Often faster than OwrenZen5() while keeping similar accuracy, but validate for your programs.
  • Vern9(): High-accuracy solver. Use for precision-critical studies and tighten tolerances.
  • BS5(): Alternative 5th-order method with robust error control.
  • DP5(): Classic 5th-order method. Can be fast, but validate carefully.
  • OwrenZen3() / OwrenZen4(): Legacy or speed-focused options.

How to select a solver

Use Options(alg=...) when you create parameters:

using GasChromatographySimulator

opt = GasChromatographySimulator.Options(alg=Tsit5(), abstol=1e-6, reltol=1e-3)
GasChromatographySimulator.Options(Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, static(false)), 1.0e-6, 0.001, "inlet", true, false, "Blumberg", "Pressure", 1.0e12)

For high-accuracy solvers (e.g. Vern9()), tighten tolerances:

opt_hi = GasChromatographySimulator.Options(alg=Vern9(), abstol=1e-8, reltol=1e-5)
GasChromatographySimulator.Options(Vern9{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, static(false), true), 1.0e-8, 1.0e-5, "inlet", true, false, "Blumberg", "Pressure", 1.0e12)

Validation and benchmarking

The script scripts/compare_ode_algorithms.jl compares multiple solvers on both a long-column case and a short-column gradient case. Use it whenever you change solver settings or want to confirm numerical equivalence across solvers.

Key guidance:

  • Validate solver changes with at least one non-gradient and one gradient case.
  • Compare both retention times (tR) and peak widths (τR).
  • If differences exceed your acceptable threshold, keep OwrenZen5() or tighten tolerances.

Example benchmark results (local tests)

Results from a representative comparison (17 solutes, "Wax" stationary phase):

  • No gradient (30 m column):

    • All solvers succeeded.
    • Max differences vs OwrenZen5() were small for Tsit5(), Vern9(), BS5(), and OwrenZen4().
    • DP5() showed larger deviations for some solutes and should be validated carefully before use.

  • With thermal gradient (2 m column, stronger ΔT):

    • All solvers succeeded.
    • Differences vs OwrenZen5() were generally smaller than in the no-gradient case for most solvers.
    • Tsit5() and Vern9() showed good agreement with the baseline.

These results are sensitive to the temperature program, column dimensions, and solute set. Always confirm solver agreement for your specific configuration.

Benchmark plots

Runtime comparison (no gradient)

Runtime (no gradient)

Max retention time differences (gradient)

Max |ΔtR| vs baseline (gradient)

Chromatogram overlays (no gradient)

Chromatogram comparison (no gradient)

Chromatogram overlays (gradient)

Chromatogram comparison (gradient)

Notes on gradients

Thermal gradients can amplify numerical differences. If you use gradients or short columns, re-check solver agreement with the gradient test case in scripts/compare_ode_algorithms.jl and tighten tolerances if needed.