ADVANCE OF SMARANDACHE APPROACH TO SOLVING SYSTEMS OF DIOPHANTlNE EQUATIONS

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and analytical formulae, which may be used for fmding numerical solutions of some combinatorial and number-theoretic problems

COMPARATIVE ANALYSIS OF EXACT AND ITERATIVE METHODS FOR SOLVIN SLAES

The numerical solution of systems of linear algebraic equations (hereinafter SLAE) is one of the most frequently encountered problems in scientific and technical research, mathematical physics (numerical solution of differential and integral equations), economics, statistics. According to modern literature, about 75% of all computational problems lead to the solution of systems of linear algebraic equations. And, accordingly, the need to choose the method of solving SLAE, giving, with the use of computer technology, an effective result is actualized. This article compares the different methods for solving SLA

Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs

We describe and analyse the parallel implementation of a novel domain decomposition preconditioner for the fast iterative solution of linear systems of algebraic equations arising from the discretization of elliptic partial differential equations (PDEs) in three dimensions. In previous theoretical work, this preconditioner has been proved to be optimal for symmetric positive-definite (SPD) linear systems. In this paper, we provide details of our three-dimensional parallel implementation and demonstrate that the technique may be generalized to the solution of non-symmetric algebraic systems, such as those arising when convection-diffusion problems are discretized using either Galerkin or stabilized finite-element methods (FEMs). Furthermore, we illustrate the potential of the preconditioner for use within an adaptive finite-element framework by successfully solving convection-dominated problems on locally, rather than globally, refined meshes

Using a small algebraic manipulation system to solve differential and integral equations by variational and approximation techniques

The microcomputer algebraic manipulation system MUMATH is used to implement the classical variational, Galerkin and least-squares techniques for solving boundary-value problems in differential equations and also for solving Fredholm integral equations. Examples are given which extend the precision of known results. The technique is presented as a general algorithm which can readily be implemented on other algebraic manipulation systems

Small Local Dynamic Fuzzy Logical Models for Large-Scale Power Systems

In the power system stability problems the primary actors in the mathematical system model are the differential equations defining the dynamic state variables of generation and load. These differential equations are coupled together by load flow equations. Mathematically the load flow equations are nonlinear algebraic equations. These differential equations and nonlinear algebraic equations form the mathematical Differential Algebraic Equations (DAE) model for the power system. The fuzzy set theory is commonly used in analysis of dynamical nonlinear systems. In this paper, we build a set of local dynamical fuzzy logic models for the differential equations, thus transforming the differential equations into nonlinear algebraic equations, the DAE into nonlinear algebraic equations. We try to simulate the system by solving the nonlinear algebraic equations rather than by solving the DAE model. We also compare the application of two types of dynamical fuzzy models: the discrete-time model and discrete-event model in this approach. First we explain the approach by a small DAE example, and then we apply it to a 10-bus power system