Liu, Ch. Hou, T. Weng, Zh.
Published in
Numerical Analysis and Applications

AbstractIn this paper, we consider \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_0^2{-}P_1$$\end{document} mixed finite element approximations of a class of nonline...

Korotov, S. Křı́žek, M.
Published in
Numerical Analysis and Applications

AbstractWe analyze red refinements of tetrahedral partitions and prove that the measure of degeneracy of some produced tetrahedra may tend to infinity if the refinements are constructed in an inappropriate way. The maximum angle condition is shown to be violated in these cases, as well.

Guemar, S. Guebbai, H. Lemita, S.
Published in
Numerical Analysis and Applications

AbstractIn this paper, we study a nonlinear integro-differential Volterra equation with the fractional Caputo derivative. Based on the techniques derived from the study of the classical Volterra equations, namely Picard’s iterative sequence and the product integration method, we propose a complete analytical and numerical analysis of this equation....

Jmeih, N. Abou Arwadi, T. El Dib, S.
Published in
Numerical Analysis and Applications

AbstractThis study aims to implement a numerical scheme in order to find the eigenvalues of the Dirichlet-to-Neumann semigroup. This can help to check the semigroup positivity for non-circular domains. This generalized scheme is analyzed after study of the case of the unit ball, in which an explicit representation for the semigroup was obtained by ...

Medvedev, I. N.
Published in
Numerical Analysis and Applications

AbstractThis paper presents algorithms of exponential transformation (biasing) and its randomized modification with branching of a Markov chain trajectory for solving problems of gamma-ray transport in an inhomogeneous medium. The algorithms are applied to the maximum (majorant) cross-section method (Woodcock tracking), which is efficient for simul...

Uddin, M. Khan, A.
Published in
Numerical Analysis and Applications

AbstractIn the present work, a numerical scheme is constructed for approximation of a class of Volterra integral equations of convolution type with highly oscillatory kernels. The proposed numerical technique transforms Volterra integral equations of convolution type into simple algebraic equations. By the inverse transform, the problem is converte...

Litvinov, V. A. Uchaikin, V. V.
Published in
Numerical Analysis and Applications

AbstractThis paper considers problems of reconstructing from known solutions the parameters of differential equations describing anomalous diffusion processes. A variational interpolation method proposed and tested by the authors earlier is used. Reconstruction of the time dependence of the diffusion coefficient and determination of the order of fr...

Kydyraliev, S. K. Sklyar, S. N. Urdaletova, A. B.
Published in
Numerical Analysis and Applications

AbstractTo numerically solve a system of linear algebraic equations with a tridiagonal matrix, a recursive version of Cramer’s rule is proposed. This method requires no additional restrictions on the matrix of the system similar to those formulated for the double-sweep method. The results of numerical experiments on a large set of test problems are...

Kozyrev, A. N. Sveshnikov, V. M.
Published in
Numerical Analysis and Applications

AbstractAn experimental study of the efficiency of solvers of 2D boundary value problems on subgrids of quasi-structured rectangular grids is carried out. A solver means a solution method and its software implementation. The following three solvers are considered: a direct solver (Buneman’s cyclic reduction method) and two iterative ones (the alter...

Aida-zade, K. R. Ashrafova, Ye. R.
Published in
Numerical Analysis and Applications

AbstractIn this paper, we investigate the problem of control of a complex object described by a large ODE system of block structure with unseparated boundary conditions between the blocks. The aim is to optimize controls in the right-hand sides of the equations and the values of the source parameters in the boundary conditions. We propose to solve ...