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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
Numerical Analysis and Applications Pub Date : 2022-12-08 DOI: 10.1134/s1995423922040048
M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky
{"title":"Solving the Pure Neumann Problem by a Mixed Finite Element Method","authors":"M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky","doi":"10.1134/s1995423922040048","DOIUrl":"https://doi.org/10.1134/s1995423922040048","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"18 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-08 DOI: 10.1134/s1995423922040073
I. V. Kireev, A. E. Novikov, E. A. Novikov
{"title":"Stability Domains of Explicit Multistep Methods","authors":"I. V. Kireev, A. E. Novikov, E. A. Novikov","doi":"10.1134/s1995423922040073","DOIUrl":"https://doi.org/10.1134/s1995423922040073","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"4 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-08 DOI: 10.1134/s199542392204005x
Kh. D. Ikramov, A. M. Nazari
{"title":"On the Sensitivity of the Canonical Angles of a Unitoid Matrix","authors":"Kh. D. Ikramov, A. M. Nazari","doi":"10.1134/s199542392204005x","DOIUrl":"https://doi.org/10.1134/s199542392204005x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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 <span>(A)</span> are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of <span>(A)</span>, which is the matrix <span>(A^{-*}A)</span>. We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in <span>(A^{-*}A)</span> caused by a perturbation in <span>(A)</span>.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"83 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040115
I. V. Boikov, A. Boikova
{"title":"Erratum to: On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals","authors":"I. V. Boikov, A. Boikova","doi":"10.1134/S1995423922040115","DOIUrl":"https://doi.org/10.1134/S1995423922040115","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"380"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46292199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040127
D. Conte, N. Guarino, G. Pagano, B. Paternoster
{"title":"Erratum to: On the Advantages of Nonstandard Finite Difference Discretizations for Differential Problems","authors":"D. Conte, N. Guarino, G. Pagano, B. Paternoster","doi":"10.1134/S1995423922040127","DOIUrl":"https://doi.org/10.1134/S1995423922040127","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"381"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42391232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-01 DOI: 10.1134/s1995423922040085
I. Klimonov, V. Sveshnikov
{"title":"Experimental Study of Some Solvers of 3D Boundary Value Subproblems on Regular Subgrids of Quasi-Structured Parallelepipedal Grids","authors":"I. Klimonov, V. Sveshnikov","doi":"10.1134/s1995423922040085","DOIUrl":"https://doi.org/10.1134/s1995423922040085","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"353-363"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42481251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-01 DOI: 10.15372/sjnm20220407
I. Kireev, A. Novikov, E. Novikov
{"title":"Stability Domains of Explicit Multistep Methods","authors":"I. Kireev, A. Novikov, E. Novikov","doi":"10.15372/sjnm20220407","DOIUrl":"https://doi.org/10.15372/sjnm20220407","url":null,"abstract":"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.","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"343-352"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45713976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
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
{"title":"Erratum to: On a Numerical Model of a Circadian Oscillator","authors":"A. Akinshin, N. Ayupova, V. Golubyatnikov, N. Kirillova, O. Podkolodnaya, N. Podkolodnyy","doi":"10.1134/S1995423922040103","DOIUrl":"https://doi.org/10.1134/S1995423922040103","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"379"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46863046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-01 DOI: 10.1134/S1995423922040024
S. A. Gusev
{"title":"On the Variance of Estimation of a Diffusion Process Functional in a Domain with a Reflecting Boundary","authors":"S. A. Gusev","doi":"10.1134/S1995423922040024","DOIUrl":"https://doi.org/10.1134/S1995423922040024","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"293 - 302"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48102696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Numerical Analysis and Applications Pub Date : 2022-12-01 DOI: 10.15372/sjnm20220409
M. Kokurin, V. V. Klyuchev
{"title":"Uniqueness Conditions and Numerical Approximation of the Solution to M. M. Lavrentiev’s Integral Equation","authors":"M. Kokurin, V. V. Klyuchev","doi":"10.15372/sjnm20220409","DOIUrl":"https://doi.org/10.15372/sjnm20220409","url":null,"abstract":"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.","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"15 1","pages":"364-378"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41978038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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