Numerical integration of ordinary differential equations of various orders

Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced

Host at Your Own Risk: Monitoring the Legality of Airbnb Rentals at the Platform Level

Article published in the Michigan State University School of Law Student Scholarship Collection

Equation-free Dynamic Renormalization of a KPZ-type Equation

In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves "lifting" from candidate pair-correlation functions to consistent realization ensembles, short bursts of KPZ-type evolution, and appropriate rescaling of the resulting averaged pair correlation functions. Both the self-similar shapes and their similarity exponents are obtained at a computational cost significantly reduced to that required to reach saturation in such systems