Numerical Analysis, № 12, 2003

The implementation of the biconjugate and the squared conjugate gradient (BiCG and CGS) preconditioned iterative methods are described for solving non-symmetric systems of linear algebraic equations (SLAEs) which arise when approximating multi-dimensional boundary value problems (BVPs) for diffusion-convection partial differential equations (PDEs), by finite eifference, finite element and finite volume...

The main objective of the paper is to present a program to solve the 3D BVP for the problem of linear thermoelasticity. Numerical algorithms for data structures, element-by-element finite volume approximations, and iterative solution are given.

The purpose of the present program is to solve a mixed boundary value problem...

We consider algorithms of numerical solution of a nonlinear system of three diffusion-convection partial differential equations (PDEs).

The paper deals with a numerical model based on the finite element discretization of the 3-D thermoelasticity problem in compound parallelepipedal domain. The piece-wise trilinear functions are used. Iterative process is based on the Neumann-Dirichlet domain decomposition procedure, and numerical experiments demonstrate that the convergence rate does not depend on...

This paper considers the software of the integer and the mixed-integer quadratic programming, which is based on the method of branches and boundaries with one-sided branching. Some examples of the solution of test problems are presented.

Modern problems of the mathematical modeling include a very wide range of computational tasks. Those tasks are based on solving different problems of mathematical physics, especially, in engineering. Such systems can be considered as passing of sets of data through the nodes of a graph. So, our task is to...

The generator of algorithms to calculate a set of Vandermonde and Hahkel algebraic structures elements is proposed.

The paper presents an algorithm for the numerical solution of the initial value problems for systems of ordinary differential equations with singular matrix multiplying the derivative. The algorithm uses the (m,k) scheme of the Rosenbrock type with time-lagging derivative matrices, and the adaptive step size control...

This paper is dealt with investigation of the numerical aspects concerned with using the vector finite element method for solving non-stationary electromagnetic problems. A special variational formulation and its discrete analogues are offered. Peculiarities of inputting a source current into such statements are considered. The results of some numerical experiments...

In this work we investigate some features of numerical implementation of the vector finite element method of lower orders for different types of elements. The comparison of data structures, computer memory requirements and application of iterative solvers for nodal and vector finite element approximations are presented.