## Interfaces and mixing – non-equilibrium dynamics and conservation laws at continuous and kinetic scales

Published in Frontiers in Applied Mathematics and Statistics

Published in Frontiers in Applied Mathematics and Statistics

This paper presents the study of singularly perturbed differential equations of convection diffusion type with non-local boundary condition. The proposed numerical scheme is a combination of classical finite difference method for the initial boundary condition and nonstandard finite difference method for the differential equations at the interior p...

Published in Frontiers in Physics

In this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented. The analog equation method is utilized to transform the linear and nonlinear convection-diffusion equation into an equivale...

Numerical simulation of light-wave propagation in double-clad rare-earth-doped fiber-lasers implies dealing with a two-point boundary value problem (BVP) with non separated boundary conditions. We show that this BVP can be solved in a simple way using Matlab BVP solver. However, this requires being able to provide to the BVP solver a relevant initi...

By taking Sugeno-derivative into account, first, we investigate the existence of solutions to the initial value problems (IVP) of first-order differential equations with respect to non-additive measure (more precisely, distorted Lebesgue measure). It particularly occurs in the mathematical modeling of biology. We begin by expressing the differentia...

Published in Russian Mathematics

In the paper, we consider a boundary value problem for a second order functional-differential equation with sufficiently general linear homogeneous boundary conditions. On the basis of the theory of semi-ordered spaces and with the help of special topological methods, we prove the existence of a unique positive solution to the problem.

Published in Lobachevskii Journal of Mathematics

AbstractThe finite element method for numerical solving two-dimensional boundary value problem is based on domain triangulation and piecewise linear approximation. The present paper describes how to minimize the number of triangulation vertices without exceeding the given level of the approximation error. The paper proposes a method for constructin...

Published in Lobachevskii Journal of Mathematics

AbstractIn this paper, we consider a boundary value problems for a systems of loaded integro-differential equations with an involutory transformation. The parameterization method is applied to the boundary value problem for a system with continuous kernel. By using the properties of involutory transformation, the problem is transformed to a boundar...

Published in Siberian Advances in Mathematics

Abstract The article is devoted to the study of boundary value problems for a fractional-order convection-diffusion equation with memory effect. We construct two-layer monotone schemes with weights of the second order accuracy with respect to the time and space variables. We prove the uniqueness and stability for the solution with respect to the in...

Published in Siberian Advances in Mathematics

Abstract The article is devoted to the study of boundary value problems for a fractional-order convection-diffusion equation with memory effect. We construct two-layer monotone schemes with weights of the second order accuracy with respect to the time and space variables. We prove the uniqueness and stability for the solution with respect to the in...