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Numerical simulation of cryosurgeries and optimization of probe placement
Pleiades Publishing Ltd - Tập 55 - Trang 1579-1589 - 2015
Numerical simulation and optimization of cryosurgeries are considered. The Stefan problem that describes thermal processes running in the course of surgery is solved numerically. The finite volume method and enthalpy approach are used. The problem of optimization of the probe positions is solved to improve the surgery efficiency. The optimization problem is solved using nonparametric multiple crit...... hiện toàn bộ
On one method for the analysis of the Cauchy problem for a singularly perturbed inhomogeneous second-order linear differential equation
Pleiades Publishing Ltd - Tập 57 - Trang 1635-1649 - 2017
A sequence converging to the solution of the Cauchy problem for a singularly perturbed inhomogeneous second-order linear differential equation is constructed. This sequence is also asymptotic in the sense that the deviation (in the norm of the space of continuous functions) of its nth element from the solution of the problem is proportional to the (n + 1)th power of the perturbation parameter. A s...... hiện toàn bộ
Multioperator representation of composite compact schemes
Pleiades Publishing Ltd - Tập 54 Số 10 - Trang 1522-1535 - 2014
The multioperator approach is used to obtain high-order accurate compact differences. These differences are developed to describe convective terms of differential equations, as well as mixed derivatives, source terms, and the coefficients of metric derivatives of coordinate transformations. The same principles are used to obtain high-order compact differences for representing diffusion terms. Thes...... hiện toàn bộ
Fast computation of optimal disturbances for duct flows with a given accuracy
Pleiades Publishing Ltd - Tập 50 Số 11 - Trang 1914-1924 - 2010
Alternating triangular schemes for convection–diffusion problems
Pleiades Publishing Ltd - Tập 56 - Trang 576-592 - 2016
Explicit–implicit approximations are used to approximate nonstationary convection–diffusion equations in time. In unconditionally stable two-level schemes, diffusion is taken from the upper time level, while convection, from the lower layer. In the case of three time levels, the resulting explicit–implicit schemes are second-order accurate in time. Explicit alternating triangular (asymmetric) sche...... hiện toàn bộ
Finite-difference proof of the completeness of eigenfunctions of the Sturm-Liouville operator in conservative form
Pleiades Publishing Ltd - Tập 55 - Trang 1-7 - 2015
A finite-difference method is used to prove the completeness of the eigenfunctions of the Sturm-Liouville operator in conservative form. The finite-difference schemes corresponding to the conservative Sturm-Liouville equation with various boundary conditions are shown to be self-adjoint. The accuracy and convergence of the method are analyzed, and the properties of eigenvalues and eigenvectors of ...... hiện toàn bộ
Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions
Pleiades Publishing Ltd - Tập 47 - Trang 180-182 - 2007
Some recent works related to the Rayleigh function are analyzed that reestablish results that have been known in the literature for over one hundred years.
Numerical implementation of an iterative method with boundary condition splitting for solving the nonstationary stokes problem on the basis of an asymptotically stable two-stage difference scheme
Pleiades Publishing Ltd - Tập 54 - Trang 1817-1825 - 2014
A new numerical implementation of a fast-converging iterative method with splitting of boundary conditions is constructed for solving the Dirichlet initial-boundary value problem for the nonstationary Stokes system. The method was earlier proposed and substantiated at the differential level by B.V. Pal’tsev. The problem is considered in a strip and is assumed to be periodic along the strip. Accord...... hiện toàn bộ
Adaptive Interpolation Algorithm Using TT-Decomposition for Modeling Dynamical Systems with Interval Parameters
Pleiades Publishing Ltd - Tập 61 - Trang 1387-1400 - 2021
Problems with inexactly specified parameters arise in many applications, and they are often formulated as dynamical systems with interval parameters. For such systems, it is required to know how to obtain an interval estimate of solution given the interval values of the parameters. The main idea underlying the adaptive interpolation algorithm is to construct an adaptive hierarchical grid based on ...... hiện toàn bộ
Numerical algorithm for solving diffusion-type equations on the basis of multigrid methods
Pleiades Publishing Ltd - Tập 50 - Trang 1367-1390 - 2010
A new numerical algorithm based on multigrid methods is proposed for solving equations of the parabolic type. Theoretical error estimates are obtained for the algorithm as applied to a two-dimensional initial-boundary value model problem for the heat equation. The good accuracy of the algorithm is demonstrated using model problems including ones with discontinuous coefficients. As applied to initi...... hiện toàn bộ
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