Levine Family Reunion Members, interviewed by Wendy Miller in September 2009: Transcript

The Levine family held an extensive reunion during the Summer of 2009 during which 29 DVDs of raw material were recorded for use in the creation of a Levine family mini-documentary. Many of these DVDs contain oral history interviews conducted by Wendy Miller, one of the organizers of the reunion. Although these interviews were not designed for historical research, they contain valuable historical information. Some of the family members interviewed include: Ben Arnon (4/5), Marjorie, Stephen, and Michael Kaplan (8), Glenyce Miller Kaplan (starts in 15, continues in 9; separate interview in 13), Burt, Phyllis, and Louis Shiro (9) [Burt Shiro also in 26/27], Myrt and Gordon Wolman (9), Ted and Billy Alfond (10), Barbara and Joan Alfond (10), Susan and Peter Alfond (10), Alice Emory [caregiver for Bibby] (11), Eric Bloom and Stu Cushner (11), Saralee Kaplan Bloom (11), Sarah Miller Arnon (12), Kayla and Jenna Cushner (12), Josh Soros and Eliana Miller-Kaplan (12), Sarah, Wendy, and Julie Miller (starts in 12, continues in 14), Bill Shutzer (13), Maschia and Glicka Kaplan, Sharon Kushner, Dan Hood (13), Gene, Alex, Kate Cohen (14), Ben, Jeremy, Joselyn Arnon (14), Wendy and Julie Miller at the store (15), and Eric Bloom (15).

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.