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On an Approach to the Numerical Solution of Dirichlet Problems of Arbitrary Dimensions 任意维狄利克雷问题数值解的一种方法
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-03-04 DOI: 10.1134/s1995423922010062
B. V. Semisalov

Abstract

A method of the numerical solution of Dirichlet boundary value problems for nonlinear partial differential equations of the elliptic type and of arbitrary dimensions is proposed. It takes little memory and computer time for problems with smooth solutions. The method is based on modified interpolation polynomials with Chebyshev nodes to approximate the sought-for function and on a new approach to constructing and solving the linear algebraic problems corresponding to the initial differential equations. The spectra and condition numbers of the matrices formed by the algorithm are analyzed by using interval methods. Theorems on approximation and stability of the algorithm are proved in the linear case. It is shown that the algorithm provides a considerable decrease in computational costs as compared to the classical collocation and finite difference methods.

摘要提出了任意维椭圆型非线性偏微分方程Dirichlet边值问题数值解的一种方法。它只需要很少的内存和计算机时间就可以顺利解决问题。该方法基于带切比雪夫节点的修正插值多项式来逼近所求函数，为构造和求解初始微分方程对应的线性代数问题提供了一种新的方法。用区间方法分析了算法形成的矩阵的谱和条件数。在线性情况下，证明了算法的逼近性和稳定性定理。结果表明，与经典的配点法和有限差分法相比，该算法的计算量大大减少。
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引用次数: 2
Non-Traditional Intervals and Their Use. Which Ones Really Make Sense? 非传统间隔及其使用。哪些是真正有意义的?
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-02-07 DOI: 10.1134/S1995423923020088
S. P. Shary
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引用次数: 0
On Matrices Whose Cosquares are Diagonalizable and Have Real Spectra 关于协平方可对角化且具有实谱的矩阵
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-01-01 DOI: 10.15372/sjnm20220104
K. Ikramov
Abstract It is shown that an algorithm for verifying the congruence of square roots of Hermitian matrices, proposed earlier by the author, can be extended to the considerably broader class of matrices whose cosquares are diagonalizable and have real spectra.
摘要证明了作者早期提出的一种验证Hermitian矩阵平方根同余的算法，可以推广到更广泛的一类共平方可对角化且具有实谱的矩阵。
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引用次数: 0
Solving Two-Dimensional Problems of Gas Dynamics Using an Implicit Scheme for the Discontinuous Galerkin Method on Unstructured Triangular Grids 用非结构三角形网格上间断Galerkin方法的隐式格式求解二维气体动力学问题
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-01-01 DOI: 10.15372/sjnm20220102
R. V. Zhalnin, V. F. Masyagin, V. Tishkin
Abstract An implicit scheme of the discontinuous Galerkin method for solving gas dynamics equations on unstructured triangular grids is constructed. The implicit scheme is based on a representation of a system of grid equations in the so-called “delta” form. To solve the resulting SLAE for each time, solvers from the NVIDIA AmgX library are used. To verify the numerical algorithm, calculations are performed for the flow over an NACA0012 symmetric airfoil at various angles of attack and the flow over an RAE2822 airfoil. The results of calculations are presented.
摘要构造了求解非结构三角形网格上气体动力学方程的间断Galerkin方法的隐式格式。隐式方案基于所谓“delta”形式的网格方程组的表示。为了求解每次产生的SLAE，使用NVIDIA AmgX库中的解算器。为了验证数值算法，对NACA0012对称翼型在不同攻角下的流动和RAE2822翼型上的流动进行了计算。给出了计算结果。
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引用次数: 0
Solving Two-Dimensional Problems of Gas Dynamics Using an Implicit Scheme for the Discontinuous Galerkin Method on Unstructured Triangular Grids 用非结构三角形网格上间断Galerkin方法的隐式格式求解二维气体动力学问题
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-01-01 DOI: 10.1134/S1995423922010025
R. V. Zhalnin, V. F. Masyagin, V. Tishkin
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引用次数: 0
On Matrices Whose Cosquares are Diagonalizable and Have Real Spectra 关于平方可对角化且具有实谱的矩阵
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-01-01 DOI: 10.1134/S1995423922010049
K. Ikramov
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引用次数: 0
On an Approach to Qualitative Analysis of Nonlinear Dynamic Systems 非线性动力系统的定性分析方法
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2022-01-01 DOI: 10.1134/S1995423922010050
V. Irtegov, T. Titorenko
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引用次数: 0
A Numerical Method for Solving Volterra Integral Equations with Oscillatory Kernels Using a Transform 用变换求解具有振荡核的Volterra积分方程的数值方法
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2021-10-01 DOI: 10.1134/S1995423921040078
M. Uddin, A. Khan
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引用次数: 1
A Priori Error Estimates of $$P_0^2{-}P_1$$ Mixed Finite Element Methods for a Class of Nonlinear Parabolic Equations 一类非线性抛物型方程$$P_0^2{-}P_1$$混合有限元法的先验误差估计
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2021-10-01 DOI: 10.1134/s1995423921040054
Ch. Liu, T. Hou, Z. Weng
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引用次数: 0
A Priori Error Analysis of a Stabilized Finite-Element Scheme for an Elliptic Equation with Time-Dependent Boundary Conditions 具有时变边界条件的椭圆型方程稳定有限元格式的先验误差分析
IF 0.3 Q4 MATHEMATICS, APPLIED
Numerical Analysis and Applications
Pub Date : 2021-10-01 DOI: 10.1134/S1995423921040017
N. A. Jmeih, T. Arwadi, S. Dib
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引用次数: 0
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