Local linearization method

Local Linearization Method

1 Local Linearization Method

In numerical analysis, the Local Linearization (LL) method is a general strategy for designing numerical inte-

grators for diferential equations based on a local (piecewise) linearization of the given equation on consecutive

time intervals. The numerical integrators are then iteratively defined as the solution of the resulting piecewise

linear equation at the end of each consecutive interval. The LL method has been development for a variety of

equations such that the ordinary, delayed, random and stochastic diferential equations. The LL integrators

are key component in the implementation of inference methods for the estimation of unknown parameters

and unobserved variables of diferential equations given time series of (potentially noisy) observations. The

LL schemes are ideals to deals with complex models in a variety of fields as neuroscience, finance, forestry

management, control engineering, mathematical statistics, etc.