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Solving the Pure Neumann Problem by a Mixed Finite Element Method 用混合有限元法求解纯诺伊曼问题
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-08 DOI: 10.1134/s1995423922040048
M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky

Abstract

This paper proposes a new method for the numerical solution of the pure Neumann problem for the diffusion equation in a mixed formulation. The method is based on the inclusion of a condition of unique solvability of the problem in one of the equations of the system with a subsequent decrease in its order by using a Lagrange multiplier. The unique solvability of the problem thus obtained and its equivalence to the original mixed formulation in a subspace are proved. The problem is approximated on the basis of a mixed finite element method. The unique solvability of the resulting system of saddle point linear algebraic equations is investigated. Theoretical results are illustrated by computational experiments.

摘要本文提出了混合公式中扩散方程纯Neumann问题数值解的一种新方法。该方法是基于用拉格朗日乘子将问题的唯一可解条件包含在系统的一个方程中，该方程的阶数随后降低。证明了该问题的唯一可解性及其在子空间上与原混合公式的等价性。在混合有限元法的基础上对问题进行了近似求解。研究了鞍点线性代数方程组的唯一可解性。计算实验验证了理论结果。
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引用次数: 0
Stability Domains of Explicit Multistep Methods 显式多步骤方法的稳定域
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-08 DOI: 10.1134/s1995423922040073
I. V. Kireev, A. E. Novikov, E. A. Novikov

Abstract

A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on the Bernoulli method for computing the greatest in magnitude root of polynomials with complex coefficients and the Dandelin–Lobachevsky–Gräffe method for squaring roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.

摘要提出了一种求解多步数值格式稳定域的新算法。该算法基于计算复系数多项式的最大数量级根的伯努利方法和计算平方根的Dandelin-Lobachevsky-Gräffe方法。给出了3-11阶Adams-Bashforth方法稳定域构造的数值结果。
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引用次数: 0
On the Sensitivity of the Canonical Angles of a Unitoid Matrix 论酉阵正则角的灵敏度
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-08 DOI: 10.1134/s199542392204005x
Kh. D. Ikramov, A. M. Nazari

Abstract

A unitoid matrix is a square complex matrix that can be brought to diagonal form by a Hermitian congruence transformation. The canonical angles of a nonsingular unitoid matrix (A) are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of (A), which is the matrix (A^{-*}A). We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in (A^{-*}A) caused by a perturbation in (A).

一元矩阵是一种可以通过厄米同余变换转化为对角形式的平方复矩阵。非奇异单位阵(A)的规范角是(直到因子1/2)(A)的余方的特征值的参数，也就是矩阵(A^{-*}A)。我们导出了由(A)中的扰动引起的(A^{-*}A)中扰动方向上的余方特征值的导数的估计。
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引用次数: 0
Erratum to: On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals 关于构造计算超奇异积分的正交公式的一种方法的勘误
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040115
I. V. Boikov, A. Boikova
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引用次数: 0
Erratum to: On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems 关于微分问题的非标准有限差分离散化的优点的勘误
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040127
D. Conte, N. Guarino, G. Pagano, B. Paternoster
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引用次数: 0
Experimental Study of Some Solvers of 3D Boundary Value Subproblems on Regular Subgrids of Quasi-Structured Parallelepipedal Grids 拟结构平行六面体网格规则子网格三维边值子问题若干求解方法的实验研究
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.1134/s1995423922040085
I. Klimonov, V. Sveshnikov
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引用次数: 0
Stability Domains of Explicit Multistep Methods 显式多步骤方法的稳定域
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.15372/sjnm20220407
I. Kireev, A. Novikov, E. Novikov
Abstract A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on the Bernoulli method for computing the greatest in magnitude root of polynomials with complex coefficients and the Dandelin–Lobachevsky–Gräffe method for squaring roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.
提出了一种求解多步数值格式稳定域的新算法。该算法基于计算复系数多项式的最大数量级根的伯努利方法和计算平方根的Dandelin-Lobachevsky-Gräffe方法。给出了3-11阶Adams-Bashforth方法稳定域构造的数值结果。
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引用次数: 0
Erratum to: On a Numerical Model of a Circadian Oscillator 对:关于昼夜节律振荡器的数值模型的勘误
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040103
A. Akinshin, N. Ayupova, V. Golubyatnikov, N. Kirillova, O. Podkolodnaya, N. Podkolodnyy
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引用次数: 0
On the Variance of Estimation of a Diffusion Process Functional in a Domain with a Reflecting Boundary 具有反射边界的区域中扩散过程泛函的估计方差
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040024
S. A. Gusev
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引用次数: 0
Uniqueness Conditions and Numerical Approximation of the Solution to M. M. Lavrentiev’s Integral Equation M. M. Lavrentiev积分方程解的唯一性条件及数值逼近
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-12-01 DOI: 10.15372/sjnm20220409
M. Kokurin, V. V. Klyuchev
Abstract M.M. Lavrentiev’s linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev’s equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallel calculations.
m.m.l avrentiev线性积分方程是由非线性系数反波传感问题的一种特殊变换而产生的。证明了正则调和函数与牛顿势由段支持的积集的完备性。作为推论，我们建立了m.m.l avrentiev方程解的唯一性和相关的波传感反问题。我们用并行计算给出了这个方程的近似解的结果。
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引用次数: 0
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