We propose a method for numerical approximation of Backward Stochastic Differential Equations. Our method allows the final condition of the equation to be quite general and simple to implement. It relies on an approximation of Brownian Motion by simple random walk.

SPECTRAL ELEMENT METHOD PART 1: NUMERICAL ALGORITHMS Aimé Fournier, Joseph Tribbia National Center for Atmospheri Resear h Boulder CO 80307-3000 USA fournier u ar.edu Mark A. Taylor Albuquerque NM 87108 USA www.s d.u ar.edu/ ss/staff/taylor ABSTRACT It is well known that the fast and a urate solution of the partial di erential equations (PDEs) governing geophysi al uid dynami s presents a great...

Quasipolynomials arise in a number of applications, and in particular as the characteristic equation associated with systems of delay differential equations. Quasipolynomial equations are generally difficult to solve, and most often must be solved numerically. In the non-trivial case, quasipolynomials have an infinite number of roots in the complex plane. We present a new numerical method for f...

Date Approved For my mother, in loving memory iii ACKNOWLEDGEMENTS The following are examples of the many people whose support has been instrumental in my completing this thesis. Joe, who offered technical, canine, and brotherly support; Becky, my wonderful and crazy sister; Dad, who accepted that in my case math wins out over physics; Mom, my favorite role model and confidante, who explained t...

Newton’s iteration has quadratic convergence for simple roots. We present a Newton-based iteration scheme with quadratic convergence for multiple roots of systems of analytic functions. This is a report on work in progress. 1. Newton Iteration, Approximate Roots and γ-Theorems 1.1. Newton Iteration. Let f : Cn → Cn be an analytic function. Newton’s method for solving f = 0 consists in approxima...

We consider a fractal scalar conservation law, that is to say, a conservation law modified by a fractional power of the Laplace operator, and we propose a numerical method to approximate its solutions. We make a theoretical study of the method, proving in the case of an initial data belonging to L∞ ∩ BV that the approximate solutions converge in L∞ weak-∗ and in Lp strong for p < ∞, and we give...

17 In this article, we present a method for determining whether a model is at least locally identifiable and in the case of non-identifiable models whether any of the parameters are individually at least locally identifiable. This method combines symbolic and numeric methods to create an algorithm that is extremely accurate compared to other numeric methods and computationally inexpensive. A se...

R esum e. La description classique du probl eme de l'optique g eom etrique est La-grangienne. Le passage a la repr esentation Eul erienne est possible mais, en pr esence de caustiques, ne permet pas de calculer la solution Lagrangienne compl ete. On pr esente le contexte math ematique du probl eme ainsi que quelques outils num eriques d evelop-p es pour lever cette limitation. Abstract. The cla...