Ordinary Differential Equations (ODE)#
An ODEProblem represents a first order ordinary differential equation (ODE) with
a given state at an initial time.
This ODEProblem is built with a function of time and state, as well as an array
describing the initial state, and a time interval.
An ODEResult represents the solution of an ODE evaluated at a discrete set of
times within the specified time interval.
Note
This feature is under active development. Future iterations include the integration of
ODEProblem s with Discipline.
Architecture#
ODEProblem and ODEResult#
The main classes in the ODE submodule are the ODEProblem and ODEResult.
These represent respectively the first-order ODE with its initial conditions, and the
solution of this problem evaluated at a discrete set of values for time.
As a reminder, a first-order ordinary differential equation is an equation of the form:
where \(s\) is the state which depends on \(t\), the time. The right-hand side function \(f\) is a function of the time and the state. The value of the state at an initial time \(t_0\) is known to be \(s_0\).
The solution of this problem is provided for discrete values of time within a given interval \([t_0,\ t_f]\).
Correspondence between the elements of an ordinary differential equation with initial
conditions and the attributes of the ODEProblem and ODEResult classes.#
Classes#
The classes described by the ODE module are as such:
Packages#
The submodules are organized in the following fashion.
