DiffEqCallbacks.jl: Prebuilt Callbacks for extending the solvers of DifferentialEquations.jl

DifferentialEquations.jl has an expressive callback system
which allows for customizable transformations of the solver behavior. DiffEqCallbacks.jl
is a library of pre-built callbacks which makes it easy to transform the solver into a
domain-specific simulation tool.

Tutorials and Documentation

For information on using the package,
see the stable documentation. Use the
in-development documentation for the version of
the documentation, which contains the unreleased features.

Manifold Projection Example

Here we solve the harmonic oscillator:

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using OrdinaryDiffEq

u0 = ones(2)
function f(du, u, p, t)
    du[1] = u[2]
    du[2] = -u[1]
end
prob = ODEProblem(f, u0, (0.0, 100.0))

However, this problem is supposed to conserve energy, and thus we define our manifold
to conserve the sum of squares:

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function g(resid, u, p, t)
    resid[1] = u[2]^2 + u[1]^2 - 2
end

To build the callback, we call

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using DiffEqCallbacks, ADTypes
cb = ManifoldProjection(g, autodiff = AutoForwardDiff(), resid_prototype = zeros(1))

Using this callback, the Runge-Kutta method Vern7 conserves energy. Note that the
standard saving occurs after the step and before the callback, and thus we set
save_everystep=false to turn off all standard saving and let the callback
save after the projection is applied.

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using Test
sol = solve(prob, Vern7(), save_everystep = false, callback = cb)
@test sol.u[end][1]^2 + sol.u[end][2]^2 ≈ 2