There is a tradeoff between speed and accuracy in fitness evaluations when various discretization sizes are used to estimate the fitness. This paper introduces discretization scheduling, which varies the size of the discretization within the GA, and compares this method to using a constant discretization. It will be shown that when scheduling the discretization, less computation time is used wi...

In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampleddata H∞ control. We formulate the discretization problem as minimization of the H∞ norm of the error system between a (delayed) target analog filter and a digital system including an ideal sampler, a zero-order hold, and a digital filter. The problem is reduced to discrete-time H∞...

This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditio...

The numerical approximation to a parabolic control problem with control and state constraints is studied in this paper. We use standard piecewise linear and continuous finite elements for the space discretization of the state, while the backward Euler method is used for time discretization. A priori error estimates for control and state are obtained by an improved maximum error estimate for cor...

There is a large variety of Local Linearization (LL) schemes for the numerical integration of initial value problems, which differ with respect to the algorithm that is used in the numerical implementation of the Local Linear Discretization. However, in contrast with the LL Discretization, the order of convergence of the LL schemes have not been studied. In this paper, a general theorem about t...

In this paper, we present a numerical scheme for a non linear FokkerPlanck equation of one-dimensional granular medium. We consider a kinetic description of a system of particles undergoing nearly elastic particles and interacting with a thermal bath. We construct a numerical method which preserve all the properties of the continuous model, conservation laws and decay of the entropy. Moreover t...

In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable crosssectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation a wellbalanced solver is deve...

The ever-widening applications of numerical calculations leads to a variety of new numerical methods, which are di erent in their solution algorithms as well as in the discretization of the governing equations. Despite this development, much work still remains in their improvement towards a fast, accurate and stable convergence. This work shows a numerical method for the solution of compressibl...

An asymptotic-induced scheme for kinetic semiconductor equations with the diiusion scaling is developed. The scheme is based on the asymptotic analysis of the kinetic semiconductor equation. It works uniformly for all ranges of mean free paths. The velocity discretization is done using quadrature points equivalent to a moment expansion method. Numerical results for diierent physical situations ...