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7 pages; 3 figures.International audienceIn this article the authors describe the method of construction of approximate chaotic solutions of dynamical model equations with quadratic nonlinearities in a general form using a new accurate numerical method. Numerous systems of chaotic dynamical systems of this type are studied in modern literature.The authors find the region of convergence of the method and offer an algorithm of construction and several criteria to check the accuracy of the approximate chaotic solutions

10 pages; 3 figures.International audienceThis paper describes a new reliable numerical method for computing chaotic solutions of dynamicalsystems and, in special cases, is applied to Chen strange attractor. The numerical precision ofthe computation is finely mastered.We introduce a modification of the method of power series forthe construction of approximate solutions of the Chen system together with forward/backwardcontrol of the precision. As a test for the method, we obtained the region of convergence ofseries and researched the behavior of the trajectories on this attractor. The results of a numericalexperiment are presented

The absolute majority of modern studies dealing with the interpretation of experimental data on the basis of the Freundlich isotherm ignore the fact that the data obtained for regions of low and moderate adsorbate concentration/pressure can be analytically continued within the Freundlich adsorption model to the adsorptive saturation area with coverages tending to 100%. Needless to say, this would give valuable extended information about the corresponding adsorption process. This message proposes a framework to comprehensively analyse experimental data first recognised as complying with the Freundlich adsorption model. An algorithm-driven method is presented which enables one to translate the data obtained in the area of small and moderate the coverages of the area of adsorptive saturation regime. As examples, three sets of experimental data for adsorption of mercury (II) on N-rich porous organic polymers and of protein on carrier nano-Mg(OH)2 have been processed and presented according to the framework developed.

In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of evolution process and reduce uncertainty. However, often used numerical methods are unable to do it on large time segments. In this article, the author considers the modern numerical method and algorithm for constructing solutions of chaotic systems on the example of tumor growth model. Also a modification of Benettin's algorithm presents for calculation of Lyapunov exponents.