  We present effective numerical algorithms for locally recovering unknown
governing differential equations from measurement data. We employ a set of
standard basis functions, e.g., polynomials, to approximate the governing
equation with high accuracy. Upon recasting the problem into a function
approximation problem, we discuss several important aspects for accurate
approximation. Most notably, we discuss the importance of using a large number
of short bursts of trajectory data, rather than using data from a single long
trajectory. Several options for the numerical algorithms to perform accurate
approximation are then presented, along with an error estimate of the final
equation approximation. We then present an extensive set of numerical examples
of both linear and nonlinear systems to demonstrate the properties and
effectiveness of our equation recovery algorithms.
