A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.This paper is partly supported by project NI13 FMI–002 of Department for Scientific Research, Paisii Hilendarski University of Plovdiv

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

ACM Computing Classification System (1998): G.1.2.Moduli for numerical finding of the polynomial of the best Hausdorff approximation of the functions which differs from zero at just one point or having one jump and partially constant in programming environment MATHEMATICA are proposed. They are tested for practically important functions and the results are graphically illustrated. These moduli can be used for scientific research as well in teaching process of Approximation theory and its application

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.Here we give methodological survey of contemporary methods for solving nonlinear systems of equations in Rn. The reason of this review is that many authors in present days rediscovered such classical methods. In particular, we consider Newton’s-type algorithms with sparse Jacobian. Method for which the inverse matrix of the Jacobian is replaced by the inverse matrix of the Vandermondian is proposed. A number of illustrative numerical examples are displayed. We demonstrate Herzberger’s model with fixed-point relations to the some discrete versions of Halley’s and Euler-Chebyshev’s methods for solving such kind of systems

On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown

A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence

Web-based Simultaneous Equation Solver

* This work has been supported by NIMP, University of Plovdiv under contract No MU-1.In this paper we present methods, theoretical basis of algorithms, and computer tools, which we have used for constructing our Web-based equation solver

Analysis of Biochemical Mechanisms using Mathematica with Applications

Biochemical mechanisms with mass action kinetics are usually modeled as systems of ordinary differential equations (ODE) or bipartite graphs. We present a software module for the numerical analysis of ODE models of biochemical mechanisms of chemical species and elementary reactions (BMCSER) within the programming environment of CAS Mathematica. The module BMCSER also visualizes the bipartite graph of biochemical mechanisms. Numerical examples, including a double phosphorylation model, are presented demonstrating the scientific applications and the visualization properties of the module. ACM Computing Classification System (1998): G.4

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.* This paper is partly supported by project IS–M–4 of Department for Scientific Research, Paisii Hilendarski University of Plovdiv

A New Modifications of the SIR/SEIR Models with ”Intervention Polynomial Factor”. Methodological Aspects

We develop a novel modification of the classic Kermack–McKendrick SIR (Susceptible–Infectious–Recovered) model. The new SIR model with ”intervention polynomial factor” (SIR-IPF) can be used successfully to model and play different scenarios for the infectious disease spread. A generalized ”reproduction number” is introduced. A similar modifications are proposed for the classic SEIR and G-SEIR models. The specialists working in the field of ”reaction-kinetic mechanisms” have the word. Numerical examples, illustrating our results are given using CAS Mathematica.Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014-2020) and co-financed by the European Union through the European structural and Investment funds

Dynamics of Modified Lotka-Volterra Model with Polynomial Intervention Factors

In the present article is considered a modification of the classical Lotka–Volterra model. The ’input functions α(t) and γ(t) are algebraic polynomials of degree n, α(t) is monotonically increasing (with ”saturation”) and γ(t) > 0 is monotonically decreasing in the considered interval. This model is very sensitive with respect to the coefficients of the polynomials a_i and b_i. Therefore it is attractive for conducting computer simulations, including other modified predator-prey models and activator-inhibitor mechanisms. Numerical examples, illustrating our results are given using CAS Mathematica.Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014- 2020) and co-financed by the European Union through the European structural and Investment funds; Grant No KP-06N42-2/27.11.2020, financed by Bulgarian National Science Fund