Chemical transformations typically occur according to multiphase schemes. Changes in theconcentrations of the starting materials and intermediates with time are not always described with increasing ordecreasing functions. A detailed study of a complex process kinetics showed that at the presence of feedback far from equilibrium there may occur vibrational modes - periodic increase or decrease in the concentration of one of the components in time. In a numerical study of oscillating reactions there appears a problem in solving a rigid system of typical differential equations. The purpose of this study is to develop an algorithm and a program to solve the direct kinetic problem and to investigate multi component chemical systems with complex nonlinear dynamics.
Based on the method of particle swarm algorithm is developed in parallel global extremum search. C
language for parallel programming in the system implements a method of particle swarm to the global
minimization of functions. The algorithm been tested on a spherical function and Rastrigin function.
The paper shows a technique of researching of the direct kinetic problem sensitivity to the variation of the
kinetic parameters within a given range. This technique is based on use of the computing device of the interval
analysis. The direct problem solution in the conditions of kinetic parameters uncertainty was received by the interval method of the solution of a Cauchy problem for differential equations system. This interval method was adapted to the problems of chemical kinetics. The interval characteristics received during this method application were used for research of reagents and products concentration sensitivity in relation to kinetic parameters of mathematical model
of industrially important reaction
An algorithm to investigate numerically the solitary wave-like solutionsof Boussinesq differential
equation is constructed. The bifurcation problem is re-formulated as an inverse problem for coefficient
identification, introducing a newparameter. Such a way the nontrivial solution is separated from the trivial
one.The Method of Variational Imbedding (MVI) is used for solving the inverse prob-lem. As illustration of the
approach a Mathematica code with the finite difference scheme is prepared and the numerical results, including verification of the scheme,connection between the solution and the coefficients, and capability of Mathematica to paralelize the algorithm are presented.
Control charts are one of the most common techniques that have been used to observe and control the
process deviations in the industry. The easiest and the most prevalent method of control charts is the Shewhart Scontrol chart. This method is based on the normal distribution assumption. However, there are a lot of inferences in literature that non-normal distributions are much more common than the normal distribution. When thenormality assumption is not satisfied robust methods are preferred. In this paper, we determine some approaches by using robust scale estimators instead of simple standard deviation in order to apply S-control charts.Furthermore the performances of these different scale estimators are compared by Monte Carlo simulation study.Numerical examples are given at the end of the paper
There are enormous occasions when the methods for finding solutions of integral and integro differential equations lead to failure because of difficulty in inverting Laplace transform by standard technique.Numerically inverting Laplace transform is cost effective in comparison to rather complicated technique of complex
analysis. In the process of numerical inversion, an odd cosine series which is ultimately based on Chebyshev
polynomial has been used. The adequacy of method is illustrated through numerical examples of convolution type linear Volterra integral equations of second kind which include weakly singular Abel's integral equation and Volterra integro-differential equation.
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