SYMBOLIC SOLUTION OF BOUNDARY VALUE PROBLEM VIA MATHEMATICA

Symbolic computation has been applied to Runge-Kutta technique in order to solve a two-point boundary value problem. The unknown boundary values are considered as symbolic variables, therefore they will appear in a system of algebraic equations, after the integration of the ordinary differential equations. Then this algebraic equation system can be solved for the unknown initial values and substituted into the solution. Consequently, only one integration pass is enough to solve the problem instead of using an iteration technique like shooting method. This procedure is illustrated by solving the boundary value problem of the mechanical analysis of a liquid storage tank. Computations were carried out by the MATHEMATICA symbolic system

FINITE ELEMENTS FOR TWO-DIMENSIONAL FREE SURFACE FLOW

The paper presents an application of the finite element method for two-dimensional shallow water circulation problem under land type boundary condition. The extended Galerkin finite element method is applied for finitization in space. To discretize time, a comparison between Heun's and Hamming's methods is given by a numerical example

SUPPORT VECTOR REGRESSION VIA MATHEMATICA

In this tutorial type paper a Mathematica function for Support Vector Regression has been developed. Summarizing the main definitions and theorems of SVR, the detailed implementation steps of this function are presented and its application is illustrated by solving three 2D function approximation test problems, employing a stronger regularized universal Fourier and a wavelet kernel. In addition, a real world regression problem, forecasting of the peak of flood-wave is also solved. The %numeric and symbolic results show how easily and effectively Mathematica can be used for solving SVR problems

Mechanikai problémákból származó nemlin. egyenletrendszerek elemzése és megoldása a MATHEMATICA integrált rendszer alkalmazásával. = Analysis and solving sets of nonlinear equations originated from mechanics using the integrated system MATHEMATICA.

A mérnöki gyakorlathoz kapcsolódó mechanikai problémák sok esetben vezetnek nemlineáris numerikus feladatra. Ilyen feladatot jelent többek között a szerkezetek stabilitásvizsgálata, a nagy elmozdulásokkal kapcsolatos vizsgálatok, illetve geodéziai eredetű számítási problémák is. Kutatásaink során megmutattuk, hogy rugalmas szerkezetek stabilitásának (egyensúlyi útjainak) vizsgálatakor a mérnöki intuícióval ellentétes eredmények is adódnak. Vizsgáltuk magas rendben szimmetrikus szerkezetek kompatibilitási, valamint nagy elmozdulásokra képes (és a DNS-molekula mechanikai modellezésére is alkalmas) hajlított-csavart rudak egyensúlyi útjait, illetve iterációs eljárást dolgoztunk ki terhelt vasbeton gerendák alakmeghatározása céljából. Elkészítettük bizonyos mérnöki feladatokban használt algoritmusok Mathematica szimbolikus-numerikus integrált rendszerbeli implementációját (pl. Bairstow-módszer, illetve a geodézia mérési hibáinak kiegyenlítésére és GPS-rendszerekben használatos "support vector regression"-módszer), igazolva ezzel a szimbolikus-numerikus rendszerek konkrét mérnöki feladatok megoldásában való hatékony alkalmazhatóságát. Mindezek alapján a PhD-képzés vonatkozó tantárgyainak anyagát is átdolgoztuk a Mathematica által a nyújtott lehetőségek figyelembe vételével. | Mechanical questions arising from engineering practice often lead to nonlinear numeric problems. This happens e.g. when stability or big displacements of a structure, as well as some computational problems coming from Geodesy are analysed. In the current research it has been shown that investigations on stability (equilibrium paths) of elastic structures sometimes give a result apparently opposed to the intuition of an engineer. Compatibility paths of highly symmetric structures and equilibrium paths of a twisted and bent rod (subject to big displacements) has also been investigated; this latter one is relevant by providing a possible mechanical model of the DNA molecule. An iterative method has been developed aiming the shape determination of loaded reinforced concrete beams as well. Some algorithms that are frequently used in engineering problems have been implemented in the Mathematica computer-algebraic system (CAS), e.g. the Bairstow method or the support vector regression method used in GPS navigation systems, thus proving the wide-spread applicability of CAS systems in solving given engineering problems. Accordingly, the material of related PhD subjects has been revised and synchronised with the options provided by Mathematica for engineers