Homotopic parametric continuation method for determining stationary states of chemical reactors with dispersion / Marek Berezowski, Marcin Lawnik // Symmetry [Dokument elektroniczny]. – 2021, Vol. 13, ... więcej

Homotopic parametric continuation method for determining stationary states of chemical reactors with dispersion / Marek Berezowski, Marcin Lawnik // Symmetry [Dokument elektroniczny]. – 2021, Vol. 13, Iss. 12, Spec. Iss., 7 s. : wykr. – Tryb dostępu: https://www.mdpi.com/2073-8994/13/12/2324. – Oznaczenie ref./art.: 2324. – Bibliogr. 18 poz., Abstr. – Special Issue: Chaotic Systems and Nonlinear Dynamics. – doi: 10.3390/sym13122324. – ISSN 2073-8994

Physical processes occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are often modeled using systems of nonlinear equations. Solving such a system ... więcej

Physical processes occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are often modeled using systems of nonlinear equations. Solving such a system is sometimes impossible in an analytical manner. The iterative methods, such as Newton’s method, are not always sufficiently effective in such cases. In this article, a combination of the homotopy method and the parametric continuation method was proposed to solve the system of nonlinear differential equations. These methods are symmetrical, i.e., the calculations can be made by increasing or decreasing the value of the parameters. Thanks to this approach, the determination of all roots of the system does not require any iterative method. Moreover, when the solutions of the system are close to each other, the proposed method easily determines all of them. As an example of the method use a mathematical model of a non-adiabatic catalytic pseudohomogeneous tubular chemical reactor with longitudinal dispersion was chosen.