ODE Problems

ODE Problems

Mathematical Specification of an ODE Problem

To define an ODE Problem, you simply need to give the function $f$ and the initial condition $u₀$ which define an ODE:

\[\frac{du}{dt} = f(u,p,t)\]

f should be specified as f(u,p,t) (or in-place as f(du,u,p,t)), and u₀ should be an AbstractArray (or number) whose geometry matches the desired geometry of u. Note that we are not limited to numbers or vectors for u₀; one is allowed to provide u₀ as arbitrary matrices / higher dimension tensors as well.

Problem Type

Constructors

Parameters are optional, and if not given then a NullParameters() singleton will be used which will throw nice errors if you try to index non-existent parameters. Any extra keyword arguments are passed on to the solvers. For example, if you set a callback in the problem, then that callback will be added in every solve call.

For specifying Jacobians and mass matrices, see the DiffEqFunctions page.

Fields

Example Problems

Example problems can be found in DiffEqProblemLibrary.jl.

To use a sample problem, such as prob_ode_linear, you can do something like:

#] add DiffEqProblemLibrary
using DiffEqProblemLibrary.ODEProblemLibrary
# load problems
ODEProblemLibrary.importodeproblems()
prob = ODEProblemLibrary.prob_ode_linear
sol = solve(prob)
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