Abstract
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.
Highlights
Physical processes and phenomena occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are modeled using systems of differential equations
The tested reactor model has three different solutions, which should be read for p = 1
This means that the reactor has three different stationary states
Summary
Physical processes and phenomena occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are modeled using systems of differential equations. For stationary states, these are Ordinary Differential Equations (ODE’s). Examples of such apparatuses are tubular chemical reactors with longitudinal dispersion. Various types of numerical methods are used to determine stationary solutions of such systems [2,3]. Determining all states (all solutions) using Newton’s method is practically impossible, especially when these states are located close to each other and there are many of them
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
