ODEConvergenceTester.jl
A simple package for testing convergence rates for OrdinaryDiffEq.jl's problems, see the integrator interface for the input arguments to OrdinaryDiffEq.init.
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Example
import OrdinaryDiffEq
# Below, `prob` `alg` and `kwargs` are the same as those passed to:
# integrator = OrdinaryDiffEq.init(prob, alg; kwargs...)
import ODEConvergenceTester
ODEConvergenceTester.refinement_study(
prob,
alg;
refinement_range = 1:3, # 2:4 is more fine than 1:3
kwargs...
)an example output might look like
[ Info: ------ Convergence parameters ------
[ Info: nsteps : [2048.0, 4096.0, 8192.0, 16384.0, 32768.0]
[ Info: refinement factors : [2.0, 2.0, 2.0, 2.0]
[ Info: dts : [0.00048828125, 0.000244140625, 0.0001220703125, 6.103515625e-5, 3.0517578125e-5]
[ Info: tfinal (rounded) : [1.0, 1.0, 1.0, 1.0, 1.0]
[ Info: --- Running convergence study... ---
@timing iteration 1: 0.000266 seconds (2.07 k allocations: 321.625 KiB)
@timing iteration 2: 0.000634 seconds (4.12 k allocations: 685.812 KiB)
@timing iteration 3: 0.001551 seconds (8.21 k allocations: 1005.812 KiB)
@timing iteration 4: 0.002754 seconds (16.41 k allocations: 2.207 MiB)
@timing iteration 5: 0.004693 seconds (32.80 k allocations: 4.881 MiB)
[ Info: ----- Convergence study output -----
[ Info: Errors : [5.610290228252879e-5, 2.8054585866632564e-5, 1.4028076611882767e-5, 7.01423422078129e-6]
[ Info: Convergence orders : [0.9998387890861984, 0.9999194015833588, 0.999959703467772]
[ Info: Expected convergence order: 1.0
[ Info: ------------------------------------
Warning
It's important that the integrator's tspan is configured carefully so that your convergence study window captures sufficient phenomena of interest. More simply:
