The task of modeling, i.e. of creating a set of equations that can be used to predict the behavior of a physical object, is a key step in engineering analysis. This paper describes a computer system, MSG, for generating mathematical models to analyze physical systems involving heat transfer behavior. MSG is motivated by the need for modeling in an automated design process. The models are sets o...

The goal of this paper is to prove a convergence rate for WongZakai approximations of semilinear stochastic partial di erential equations driven by a nite dimensional Brownian motion.

The suitability of methods from multidimensional systems theory and digital signal processing for the e cient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial di erential equation into a transfer function description of a multidimensional continuous system. It serves as the...

The Finite Di erence Time Domain (FDTD) method belongs to numerical applications that can be described by irregular data patterns or use irregular data structures. This method is based on an iterative algorithm, which is used to simulate high frequency electromagnetic wave propagation. Such simulation is performed by solving Maxwell equations transformed into their di erential form. In order to...

We construct numerical methods to integrate ordinary di erential equations that evolve on Lie groups. These schemes are based on exponentials and iterated commutators, they are explicit and their order analysis is relatively simple. Thus we can construct group-invariant integrators of arbitrarily high order. Among other applications we show that this approach can be used to obtain new symplecti...

Smoothed Particle Hydrodynamics SPH is a meshless Lagrangian parti cle method for solving a system of hydrodynamic equations for compressible uids SPH is especially suited for problems with free boundaries a commonplace situation in as trophysics Rather than solving the equations on a grid the equations are solved at the positions of the so called particles each representing a mass packet with ...

This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

We describe an object oriented MATLAB toolbox for solving di erential equations on manifolds. The software re ects recent development within the area of geometric integration. Through the use of elements from di erential geometry, in particular Lie groups and homogeneous spaces, coordinate free formulations of numerical integrators are developed. The strict mathematical de nitions and results a...

A system of a parabolic partial di erential equation coupled with ordinary di erential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn di usion reaction model is studied. A feedback law for the closed-loop control is proposed and implemented in the case of a nite number of control devices located inside the process domain basing o...