This paper investigates the qualitative properties of self-similar solutions of a nonlinear cross-diffusion system with nonlinear boundary conditions and a source. A self-similar solution of the cross-diffusion problem is constructed. In the case of global solvability, the leading term of the asymptotics of self-similar solutions of the cross-diffusion problem with a source is obtained. When numerically solving nonlinear problems using iterative methods, it is crucial to choose a suitable initial approximation that preserves the nonlinear properties. Computational experiments have shown the rapid convergence of the iterative process to the exact solution, due to the choice of a suitable initial approximation. The use of asymptotic formulas as initial approximations in iterative methods significantly increases the chances of rapid convergence of the algorithm and improves the accuracy of the numerical results obtained.
| Mualliflar | Rakhmonov, Z.R., Urunbaev, J.E., Рахмонов, З.Р., Урунбаев, Ж.Э. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2024-07-19 |
| Son | 3 |
| Betlar | 114-121 |
| Til | Rus |
asymptotics, cross-diffusion, nonlinear system, self-similar solution, iteration, кросс диффузии, асимптотика, нелинейные граничные условия, начальные приближения
Computer virology and its formalization began seventy years ago with the work of Alan Turing. The work and results of von Neumann, Fred Cohen, Leonard Adleman, and others who followed them were groundbreaking. They…
Problems of nonlinear vibrations of products lying on a viscoelastic layer are considered. A mathematical model was constructed in the form of systems of nonlinear integro-differential equations. The main quadratic…
In this article, the numerical simulation of a boundary value problem for a fourth order inhomogeneous differential equation with a small parameter at the highest deriva tive is carried out using the preliminary…
A related conjugate problem is to ensure that industrial facilities are optimally located throughout a region, taking into account global and local sanitary standards. The main parameters for the spread of harmful…
This article presents a numerical model and calculation algorithm for solving the problem of two-dimensional oil filtration in a porous medium, in which the change in permeability value when changing reservoir pressure…
The problem of the impact of a longitudinal wave on a system consisting of successively located wells and pipelines of finite length, interacting with soil by elastic-viscous law is considered in the article. The ends…
Today it is much more difficult to imagine life without computers. There is not a single area that a computer cannot penetrate. Everyday life is rapidly digitizing and unfortunately, more and more people among us are…
A mathematical model for calculating the vibrations of three-layer rods under spatial loading is developed in the article. Variations of kinetic and potential energies and the work of external forces, substituted into…
Based on the developed mathematical software, this paper presents the results of numerical calculations on the task of monitoring and forecasting the concentration of industrial emissions of pollutants (CO2, dust…
The article covers the theoretical and practical aspects of the mathematical model for predicting the movement and level of underground water based on the studied literature. An improved mathematical model based on…