Solving initial value problem by different numerical methods

Our aim was to study what kind of bases can be provided to understand the basic terms of differential equation through teaching mathematical material in secondary school and to what extent this basis has to be expanded so that we can help the demonstration of differential equation. So if we give up the usual expansion of mathematical device we have to find another method which is easy to algorithmise and lies on approach. Such method and its practical experience are shown in this paper. AMS Classification Number: 65L05, 65L06, 53A04, 97D9

Modelling a simple continuous-time system

The aim of the present paper is to give a very simple example how we can set up a mathematical model describing a not too complicated phenomenon based on measurement. It may help the beginners to model other systems too, by differential equations. At the some time we would like to enrich the possibility of demonstration in this field

Solving ordinary differential equation systems by approximation in a graphical way

Our aim was to find a graphic numeric solution method for higher-order differential equations and differential equation systems. To understand this method the basic mathematical knowledge taught in the secondary school must be enough, we have to complete it with geometric meaning of differential quotient and generalization of knowledge about two-dimensional vector space. We considered it important to make this method easy to algorithm. Such method and its practical experience are shown in this paper

Cube-and-Conquer approach for SAT solving on grids

Our goal is to develop techniques for using distributed computing re- sources to efficiently solve instances of the propositional satisfiability problem (SAT). We claim that computational grids provide a distributed computing environment suitable for SAT solving. In this paper we apply the Cube and Conquer approach to SAT solving on grids and present our parallel SAT solver CCGrid (Cube and Conquer on Grid) on computational grid infrastructure. Our solver consists of two major components. The master application runs march_cc, which applies a lookahead SAT solver, in order to partition the input SAT instance into work units distributed on the grid. The client application executes an iLingeling instance, which is a multi-threaded CDCL SAT solver. We use BOINC middleware, which is part of the SZTAKI Desktop Grid package and supports the Distributed Computing Application Programming Interface (DC-API). Our preliminary results suggest that our approach can gain significant speedup and shows a potential for future investigation and development. Keywords: grid, SAT, parallel SAT solving, lookahead, march_cc, iLingeling, SZTAKI Desktop Grid, BOINC, DC-AP