Numerical Modelling of The System of Doubly Nonlinear Diffusion Equations with Convective Transfer and Damping

Currently, studies of double nonlinear equations and systems of double nonlinear equations representing many processes found in nature are considered relevant and necessary. These equations and systems, as a rule, are nonlinear, degenerate, and have properties that are absent in linear theory and therefore make them quite difficult for both analytical and numerical analysis of the solution. For this reason, great attention is paid to the research of nonlinear mathematical models, the construction of efficient numerical solution schemes and algorithms, and the creation of software using the capabilities of computer technologies. In this article, the mathematical model of the diffusion process in a two-component nonlinear medium under the influence of time-dependent convective transfer and damping is studied. The calculation scheme, algorithm, and software for nonlinear problems were developed. Based on a study of the qualitative properties of a nonlinear mathematical model of a reaction-diffusion system, computer modeling of reaction-diffusion processes was carried out. The developed computational schemes, algorithms, and software packages for solving systems of parabolic equations with double nonlinearity provide high productivity in studying the theory and processes of numerical solutions of such problems.