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:

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

f should be specified as f(t,u) (or in-place as f(t,u,du)), 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

ODEProblem{isinplace}(f,u0,tspan,callback=CallbackSet(),mass_matrix=I) : Defines the ODE with the specified functions. isinplace optionally sets whether the function is inplace or not. This is determined automatically, but not inferred.

Fields

f: The function in the ODE.
u0: The initial condition.
tspan: The timespan for the problem.
callback: A callback to be applied to every solver which uses the problem. Defaults to nothing.
mass_matrix: The mass-matrix. Defaults to I, the UniformScaling identity matrix.

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:

# Pkg.add("DiffEqProblemLibrary")
using DiffEqProblemLibrary
prob = prob_ode_linear
sol = solve(prob)

DiffEqProblemLibrary.prob_ode_linear
DiffEqProblemLibrary.prob_ode_2Dlinear
DiffEqProblemLibrary.prob_ode_bigfloatlinear
DiffEqProblemLibrary.prob_ode_bigfloat2Dlinear
DiffEqProblemLibrary.prob_ode_large2Dlinear
DiffEqProblemLibrary.prob_ode_2Dlinear_notinplace
DiffEqProblemLibrary.prob_ode_threebody
DiffEqProblemLibrary.prob_ode_pleides
DiffEqProblemLibrary.prob_ode_vanderpol
DiffEqProblemLibrary.prob_ode_vanderpol_stiff
DiffEqProblemLibrary.prob_ode_rober
DiffEqProblemLibrary.prob_ode_rigidbody