A detailed description is given of the parallel algorithms used in AUTO94P, an experimental parallel version of the software AUTO for the numerical bifurcation analysis of systems of ordinary di erential equations. Timing results and user instructions for the Intel Delta are included. The sequential version of the software, AUTO94, is fully described in [8]. For a related tutorial paper see [5,...

A detailed description is given of the parallel algorithms used in AUTO94P, an experimental parallel version of the software AUTO for the numerical bifurcation analysis of systems of ordinary di erential equations. Timing results and user instructions for the Intel Delta are included. The sequential version of the software, AUTO94, is fully described in [8]. For a related tutorial paper see [5,...

This report presents an experimental comparison of NAG Fortran Library software for the solution of large sparse unsymmetric linear systems of algebraic equations Preconditioned RGMRES CGS and Bi CGSTAB methods to be introduced at Mark are compared against one another and against direct methods Test problems include discrete approximations to D elliptic partial di erential equations random valu...

The SMF methods of Mart n and Ferr andiz [SIAM J. Numer. Anal. 34 (1997) 359-375], for di erential equations of second order, are shown to be equivalent to modi ed Adams methods. This leads to new formulae for the coe cients of those methods, generating functions analogous to those of the Adams methods for equations of rst order, and simpler, more instructive, expressions for the local truncati...

We consider cyclic nearest neighbor systems of di erential delay equations, in which the coupling between neighbors possesses a monotonicity property. Using a discrete (integer-valued) Lyapunov function, we prove that the Poincar e-Bendixson theorem holds for such systems. We also obtain results on piecewise monotonicity and stability of periodic solutions of such systems.

This paper presents a family of Runge{Kutta type integration schemes of arbitrarily high order for di erential equations evolving on manifolds. We prove that any classical Runge{Kutta method can be turned into an invariant method of the same order on a general homogeneous manifold, and present a family of algorithms that are relatively simple to implement.

We present an introduction to mathematical Finance Theory for math ematicians The approach is to start with an abstract setting and then introduce hypotheses as needed to develop the theory We present the basics of European call and put options and we show the connection between American put options and backwards stochastic di erential equations

Recent developments of mathematical study for nonlinear PDEs (partial di↵erential equations) provide new ideas and various techniques based on calculus of variations, dynamical systems, asymptotic analysis, qualitative theory etc. In this session we bring together researchers in this research area to present new results for nonlinear parabolic and elliptic equations arising from mathematical sc...

We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial di/erential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature 1ow equation and apply to more general Neumann-type boundary problems for parabolic equations in the ...

This paper presents a new method for solving di erential algebraic equation systems using a mixed symbolic and numeric approach Discretization formu lae representing the numerical integration algorithm are symbolically inserted into the di erential algebraic equation model The symbolic formulae manipulation algorithm of the model translator treats these additio nal equations in the same way as ...