LOSDAR is a multistep method for solving explicit ordinary differential equations on the form,

\[\dot{y} = f(t,y), \quad y(t_0) = y_0.\]LSODAR automatically switches between using an ADAMS method or an BDF method and is also able to monitor events.

LSODAR is part of ODEPACK, http://www.netlib.org/odepack/opkd-sum

- State events (root funtions) : True
- Step events (completed step) : True
- Time events : True

Import the solver together with the correct problem:

```
from assimulo.solvers import LSODAR
from assimulo.problem import Explicit_Problem
```

Define the problem, such as:

```
def rhs(t, y): #Note that y are a 1-D numpy array.
yd = -1.0
return N.array([yd]) #Note that the return must be numpy array, NOT a scalar.
y0 = [1.0]
t0 = 1.0
```

Create a problem instance:

```
mod = Explicit_Problem(rhs, y0, t0)
```

Note

For complex problems, it is recommended to check the available examples and the documentation in the problem class, `Explicit_Problem`

. It is also recommended to define your problem as a subclass of `Explicit_Problem`

.

Warning

When subclassing from a problem class, the function for calculating the right-hand-side (for ODEs) must be named *rhs* and in the case with a residual function (for DAEs) it must be named *res*.

Create a solver instance:

```
sim = LSODAR(mod)
```

Modify (optionally) the solver parameters.

Parameters:

`atol`

Defines the absolute tolerance(s) that is to be used by the solver.`backward`

Specifies if the simulation is done in reverse time.`clock_step`

Specifies if the elapsed time of an integrator step should be timed or not.`display_progress`

This option actives output during the integration in terms of that the current integration is periodically printed to the stdout.`maxh`

The absolute value of the maximal stepsize for all methods Parameters:: maxh - Default: 0.`maxordn`

The maximum order used by the Adams-Moulton method (nonstiff case) Parameters:: maxordn - Default 12 - Should be a positive integer.`maxords`

The maximum order used by the BDF method (stiff case) Parameters:: maxords - Default 5 - Should be a positive integer.`maxsteps`

The maximum number of steps allowed to be taken to reach the final time.`num_threads`

This options specifies the number of threads to be used for those solvers that supports it.`report_continuously`

This options specifies if the solver should report the solution continuously after steps.`rkstarter`

This defines how LSODAR is started.`rtol`

Defines the relative tolerance that is to be used by the solver.`store_event_points`

This options specifies if the solver should save additional points at the events, \(t_e^-, t_e^+\).`time_limit`

This option can be used to limit the time of an integration.`usejac`

This sets the option to use the user defined jacobian.`verbosity`

This determines the level of the output.

Methods:

Simulate the problem:

Information:

`LSODAR.get_options()`

Returns the current solver options.`LSODAR.get_supports()`

Returns the functionality which the solver supports.`LSODAR.get_statistics()`

Returns the run-time statistics (if any).`LSODAR.get_event_data()`

Returns the event information (if any).`LSODAR.print_event_data()`

Prints the event information (if any).`LSODAR.print_statistics()`

Prints the run-time statistics for the problem.