BoundaryValueDiffEq

BoundaryValueDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds the boundary value problem solvers and utilities. While completely independent and usable on its own, users interested in using this functionality should check out DifferentialEquations.jl.

BoundaryValueDiffEq.jl is part of the SciML common interface, but can be used independently of DifferentialEquations.jl. The only requirement is that the user passes a BoundaryValueDiffEq.jl algorithm to solve. For example, we can solve the BVP tutorial from the documentation using the MIRK4() algorithm:

using BoundaryValueDiffEq
tspan = (0.0, pi / 2)
function simplependulum!(du, u, p, t)
    θ = u[1]
    dθ = u[2]
    du[1] = dθ
    du[2] = -9.81 * sin(θ)
end
function bc!(residual, u, p, t)
    residual[1] = u[:, end ÷ 2][1] + pi / 2
    residual[2] = u[:, end][1] - pi / 2
end
prob = BVProblem(simplependulum!, bc!, [pi / 2, pi / 2], tspan)
sol = solve(prob, MIRK4(), dt = 0.05)

For the list of available solvers, please refer to the DifferentialEquations.jl BVP Solvers page. For options for the solve command, see the common solver options page.

Precompilation can be controlled via Preferences.jl

• PrecompileMIRK -- Precompile the MIRK2 - MIRK6 algorithms (default: true).
• PrecompileShooting -- Precompile the single shooting algorithms (default: true).
• PrecompileMultipleShooting -- Precompile the multiple shooting algorithms (default: true).
• PrecompileMIRKNLLS -- Precompile the MIRK2 - MIRK6 algorithms for under-determined and over-determined BVPs (default: true).
• PrecompileShootingNLLS -- Precompile the single shooting algorithms for under-determined and over-determined BVPs (default: true).
• PrecompileMultipleShootingNLLS -- Precompile the multiple shooting algorithms for under-determined and over-determined BVPs (default: true ).

To set these preferences before loading the package, do the following (replacing PrecompileShooting with the preference you want to set, or pass in multiple pairs to set them together):

using Preferences, UUIDs
Preferences.set_preferences!(
    UUID("764a87c0-6b3e-53db-9096-fe964310641d"), "PrecompileShooting" => false)

We include a small set of benchmarks in the benchmarks folder. These are not extensive and mainly used to track regressions during development. For more extensive benchmarks, see the SciMLBenchmarks repository.

To run benchmarks locally install AirspeedVelocity.jl and run the following command in the package directory:

benchpkg BoundaryValueDiffEq --rev="master,<git sha for your commit>" --bench-on="master"