Home – Home – Jornals – Numerical Analysis and Applications 2026 number 1

Nekrasov matrices, as a subclass of H-matrices, exhibit unique functionalities and hold significant importance in diverse fields. These matrices are characterized by their distinctive structure, which endows them with numerous remarkable properties. This paper extends the study of Nekrasov matrices by introducing a new subclass of H-matrices, termed DN-matrices, and explores their properties, particularly focusing on the Schur complement.

In this paper, we consider two-dimensional multi-term time-space fractional diffusion-wave equations. We develop an alternating direction implicit (ADI) spectral method based on Legendre spectral approximation in space and finite difference discretization in time. We also prove the numerical stability and convergence of the developed scheme and that the error is O(τ²+N^γ-r), where Ν,τ,γ,r are the polynomial degree, time step size, Riesz derivative order and the regularity of the exact solution, respectively.

A continuous-discrete stochastic model describing the dynamics of a spatially heterogeneous population is presented. The individuals of the population are located in a system consisting of two interconnected compartments. The individuals move between the compartments along unidirectional pipes. The duration of individual motion along the pipes is specified by constants or functions depending on time. The individuals located in the second compartment can contact one of the reproduction centers located in this compartment. As a result of contact with a reproduction center, an individual begins the process of fission. The reproduction of the individuals arising due to fission occurs until the number of descendants exceeds a threshold level, otherwise the reproduction of individuals ends. The population formed after the completion of fission contains descendant individuals that are not subject to fission and leave the system over time. The assumptions of the model are formulated, a probabilistic formalization of the model and an algorithm of numerical modeling based on the Monte Carlo method are given. The results of a computational experiment to simulate the dynamics of the population depending on the parameters of the model are presented.

For an isotropic random field a simple computer-efficient grid model is developed which provides sufficiently high accuracy of solutions to stochastic transport problems for small correlation lengths. Results of test estimation of the time asymptotics of mean particle flux in a random multiplying medium are presented.

In this paper, we explore a double-step method for solving nonlinear equations containing a differentiable and non-differentiable operator. Our approach is built upon a combination of three different methods. We have analyzed the local convergence of the suggested method, considering both Lipschitz and L-average conditions & established the superquadratic (≈ 2.414) order of convergence. Finally we have pictured numerical results in comparison with several existing methods.

The paper considers an algorithm for numerical solving of a one-dimensional inverse magnetotelluric sounding problem. The algorithm is based on a special type of algebraic equation which is called a pseudo-quadratic equation. The inverse problem is considered in three variants: 1) for media with fixed geometry; 2) for media with fixed geoelectrical properties; 3) general case. Additionally, an algorithm is proposed for input data processing which provides the existence of a solution to the inverse problem. Numerical experiments realized on test media with different sets of parameters are carried out to study and illustrate the efficiency of the proposed algorithms.

The paper is devoted to modeling the propagation of seismic waves in a chemically inert elastically deformable rock. Only changes in stress and pore pressure are considered, and the chemistry of the saturating pore fluid does not directly affect the deformation of the rock. Chemical effects are taken into account by changing pore pressure and rock deformation in the transport equations. In the numerical solution of the problem under consideration, an algorithm is used to combine a Laguerre integral transform method and a finite difference method. The paper presents results of modeling of the transport of a dissolved substance through a semi-permeable clay shale.