A Julia wrapper for the DOPRI5 and DOP853 integrators.
4 Stars
Updated Last
8 Months Ago
Started In
November 2014

This package is deprecated and will not be maintained anymore because all use cases are covered by the DifferentialEquations.jl ecosystem.


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Dopri.jl is a Julia wrapper for the DOPRI5 and DOP853 integrators by Ernst Hairer.


Dopri.jl can then be installed through Julia's package manager. On Linux and macOS you need to have either Gfortran or the Intel Fortran Compiler installed to be able to build the binary dependencies.



The API is modelled after that of ODE.jl.

tout, yout = dopri5(F!, y0, tspan; keywords...)
tout, yout = dop853(F!, y0, tspan; keywords...)

The only differences are the mutating user function F! (see below) and a few additional keyword arguments.

The following keyword arguments are supported:

  • atol: Vector of absolute tolerances. Default: sqrt(eps()).
  • rtol: Vector of realtive tolerances. Default: 1e-6.
  • points
    • = :all: Output is given for each value in tspan and all intermediate solver steps.
    • = :specified: Output is given for each value in tspan.
    • = :last: Output is given for the final step only.
  • solout: User function that is called after every successfull integration step (see below).
  • dense: Vector of indices for which dense output shall be performed. Default: Dense output is provided for all components. Is also set automatically for points=:specified and points=:all.
  • verbose: Print messages from DOPRI5 and DOP853. Default: false.

User Functions

F!(f, t, y) = ...
  • f: f=dy/dt
  • t: Current step.
  • y: Current state vector.
solout!(told, t, y, contd) = ... return dopricode[:nominal]

If the user supplies a solout function, it will be called after every successful integration step. Within solout the contd function can be used to approximate state vector components between the current and the preceding integration step via dense output.

  • told: Last step.
  • t: Current step.
  • y: Current state vector.
  • contd: yi = contd(i, t1) Get dense output yi for component i at t1 with told < t1 < t.

solout must return one of the following return codes:

  • dopricode[:nominal]: If the integration shall continue nominally.
  • dopricode[:altered]: If numerical solution was altered in solout.
  • dopricode[:abort]: If the integration shall be stopped.

Passing Additional Parameters to User Functions

A closure can be used to pass additional parameters to the user functions, e.g.:

parameter = pi
tout, yout = dop853((f, t, y) -> F!(f, t, y, parameter), y0, tspan)