During the last few years, di erent approaches for integrating ordinary di erential equations on manifolds have been published. In this work, we consider two of these approaches. We present some numerical experiments showing bene ts and some pitfalls when using the new methods. To demonstrate how they work, we compare with well known classical methods, e.g. Newmark and Runge-Kutta methods. AMS ...

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...

In this paper we deene a compositional semantics for a generalized composition operator on logic programs. Static and dynamic inheritance as well as composition by union of clauses can all be obtained by specializing the general operator. The semantics is based on the notion of diierential programs, logic programs annotated with declarations that establish the programs' external interfaces.

In this paper we present an approach for the numerical solution of Delay Di erential Equations y 0 (t) = Ly (t) +My (t ) t 0 y (t) = ' (t) t 0; (1) where > 0, L;M 2 C I m m and ' 2 C ([ ; 0] ; C I m ), di erent from the classical step-by-step method. We restate (1) as an abstract Cauchy problem and then we discretize it in a system of Ordinary Differential Equations. The scheme of discretizatio...

Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar di usion ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the more traditional stream function-vorticity approach. The numerical solution of th...

Multidimensional wave digital lters yield robust algorithms for the computer simulation of certain distributed parameter systems described by partial di erential equations. Here, a multidimensional wave digital lter algorithm for the spacetime discretization of the physical laws of acoustics is discussed. Its implementation by state equations is presented. An example for the propagation of a so...

ADi erentially controlled monolithic LC-VCO along with a di erential charge pump are used to implement a di erential PLL for substrate noise immunity. The di erential VCO control is achieved with minimal increase in the power consumption and without sacri cing the tuning range. In a 0.5 m CMOS technology the measured VCO phase noise is -119dBc @1.0MHz and the tuning range is 26% of the 1.25GHz ...

In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid ...

This report presents experimental results for new NAG Fortran Library software for the solution of large sparse symmetric linear systems of algebraic equations Preconditioned conjugate gradient methods introduced at Mark are compared against iterative and direct methods previously available in the library Test problems include discrete approximations to d elliptic partial di erential equations ...

Optimal control theory of partial di erential equations has emerged as a new way to attack problem of D atmospheric oceanic data assimilation problems These variational techniques attempt to achieve a best t between data observations and forecast model subject to some a priori criteria This review paper presents new trends for utilizing model adjoint equations for variational data assimilation ...