Graduate Students Seminar

Speaker 1: Zainab Almutawa

Title

An Introduction to Finite Difference Method

Abstract

In this presentation, I will introduce a finite difference method, that is one of the methods to solve differential equations numerically. I will analyze a second order accurate finite difference scheme for a two-point value problem. The proposed scheme employs the standard central difference to approximate the second derivative for all mesh points away from the boundary. The local truncation error is also second order convergent, and I will provide how the truncation error determines the order of the numerical scheme. Within the proof, I will apply the discrete maximum principle to show the stability of the approximate solution obtained by the proposed scheme, this principle ensures the solution attains its extremes at the domain boundary. On the other hand, solution stability is important because it provides an upper bound for the approximate solution, this bound depends on the problem data.  At the end, I will go over some advantages and disadvantages the method does have.

Speaker 2: Ryan Lafferty

Title

Fraud Detection with the Newcomb-Benford Distribution

Abstract

In this talk I will give a non-technical overview of a method for detecting fabricated or fraudulent data. According to Benford's law, many kinds of naturally generated datasets have the interesting property that the distribution of their leading digits follows a certain distribution called the Newcomb-Benford distribution. This property has been observed in records of financial transactions, lengths of riverbeds, populations of cities, stock prices, tables of physical constants, and so on. However, when a human tries to create data that seem random, one will most often tend to choose digits more or less uniformly, causing deviation from the Newcomb-Benford distribution.  This suggests a way of detecting fabricated data by testing the digits in the data of interest for goodness of fit with the Newcomb-Benford distribution. The method has been applied to forensic accounting, election fraud and other areas. I will discuss the idea behind the test, the assumptions needed for it to work, some basic testing procedures that are commonly used, and some examples where it has been applied in real-life settings.