# IDA¶

This class provides a connection to the Sundials (https://computation.llnl.gov/casc/sundials/main.html) solver IDA.

IDA is a variable-order, variable-step multi-step algorithm for solving differential algebraic equations of the form,

$F(t,y,\dot{y})=0, \quad y(t_0) = y_0, \quad \dot{y}(t_0) = \dot{y}_0.$

IDA includes the Backward Differentiation Formulas (BDFs).

## Support¶

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

## Usage¶

Import the solver together with the correct problem:

from assimulo.solvers import IDA
from assimulo.problem import Implicit_Problem


Define the problem, such as:

def res(t, y, yd): #Note that y and yd are 1-D numpy arrays.
res = yd[0]-1.0
return N.array([res]) #Note that the return must be numpy array, NOT a scalar.

y0  = [1.0]
yd0 = [1.0]
t0  = 1.0


Create a problem instance:

mod = Implicit_Problem(res, y0, yd0, t0)


Note

For complex problems, it is recommended to check the available examples and the documentation in the problem class, Implicit_Problem. It is also recommended to define your problem as a subclass of Implicit_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 = IDA(mod)


Modify (optionally) the solver parameters.

Parameters:

Methods:

Simulate the problem:

Information: