Usage¶
To use ode:
import ode
Examples¶
Classes and functions¶
-
ode.Euler(dfun, xzero, timerange, timestep)[source]¶ Euler method integration. This class implements a generator.
- Parameters
dfun – derivative function of the system. The differential system arranged as a series of first-order equations: \(\dot{X} = \mathrm{dfun}(t, x)\). Returns \(\dot{X}\) should be a single dimensional array or list.
xzero – the initial condition of the system
timerange – the start and end times as (starttime, endtime) tuple/list/array.
timestep – the timestep
- Returns
t, x for each iteration. t is a number. x is an array.
-
ode.euler(dfun, xzero, timerange, timestep)[source]¶ Euler method integration. This function wraps the Euler class.
- Parameters
All – All parameters are identical to the Euler class above.
- Returns
t, x as arrays.
-
ode.BackwardEuler(dfun, xzero, timerange, timestep, convergencethreshold=1e-10, maxiterations=1000)[source]¶ Backward Euler method integration. This class implements a generator.
- Parameters
dfun – Derivative function of the system. The differential system arranged as a series of first-order equations: \(\dot{X} = \mathrm{dfun}(t, x)\)
xzero – The initial condition of the system.
vzero – The initial condition of first derivative of the system.
timerange – The start and end times as (starttime, endtime).
timestep – The timestep.
convergencethreshold – Each step requires an iterative solution of an implicit equation. This is the threshold of convergence.
maxiterations – Maximum iterations of the implicit equation before raising an exception.
- Returns
t, x for each iteration.
-
ode.backwardeuler(dfun, xzero, timerange, timestep)[source]¶ Backward Euler method integration. This function wraps BackwardEuler.
- Parameters
All – All parameters are identical to the BackwardEuler class above.
- Returns
t, x as arrays.
-
ode.Verlet(ddfun, xzero, vzero, timerange, timestep)[source]¶ Verlet method integration. This class implements a generator.
- Parameters
ddfun – second derivative function of the system. The differential system arranged as a series of second-order equations: \(\ddot{X} = \mathrm{dfun}(t, x)\)
xzero – the initial condition of the system
vzero – the initial condition of first derivative of the system
timerange – the start and end times as (starttime, endtime)
timestep – the timestep
- Returns
t, x, v for each iteration.