Compatible convergence estimates in the method of refinement by higher-order differences

被引：5
|
作者：
Berikelashvili, G. K. [1 ]
Midodashvili, B. G. [1 ]
机构：
[1] Tbilisi State Univ, GE-380086 Tbilisi, Georgia
来源：
DIFFERENTIAL EQUATIONS | 2015年 / 51卷 / 01期
关键词：
SCHEMES;
D O I：
10.1134/S0012266115010103
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Dirichlet problem for an elliptic equation with constant coefficients, which is solved by a difference scheme of second-order accuracy. By using the approximate solution, we correct the right-hand side of the difference scheme. We show that the solution of the corrected scheme is convergent at the rate O(|h| (m) ) in the discrete L (2)-norm provided that the solution of the original problem belongs to the Sobolev space with exponent m a [2, 4].
引用
收藏
页码：107 / 115
页数：9
相关论文
共 50 条
  • [1] Compatible convergence estimates in the method of refinement by higher-order differences
    G. K. Berikelashvili
    B. G. Midodashvili
    Differential Equations, 2015, 51 : 107 - 115
  • [2] Convergence and Dynamics of a Higher-Order Method
    Moysi, Alejandro
    Argyros, Ioannis K.
    Regmi, Samundra
    Gonzalez, Daniel
    Alberto Magrenan, A.
    Antonio Sicilia, Juan
    SYMMETRY-BASEL, 2020, 12 (03):
  • [3] CONVERGENCE PROPERTIES OF HIGHER-ORDER MOMENT AND CUMULANT ESTIMATES
    Li Hongwei(Institute of Information Science
    Journal of Electronics(China), 1998, (03) : 240 - 247
  • [4] Convergence and error estimates for the series solutions of higher-order differential equations
    Ma, Junchi
    Liang, Songxin
    Zhang, Xiaolong
    Zou, Li
    JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2017, 23 (04) : 647 - 659
  • [5] Refinement of higher-order logic programs
    Colvin, R
    Hayes, I
    Hemer, D
    Strooper, P
    LOGIC BASED PROGRAM SYNTHESIS AND TRANSFORMATION, 2003, 2664 : 126 - 143
  • [6] A NEW CONVERGENCE PROOF FOR THE HIGHER-ORDER POWER METHOD AND GENERALIZATIONS
    Uschmajew, Andre
    PACIFIC JOURNAL OF OPTIMIZATION, 2015, 11 (02): : 309 - 321
  • [7] Boundary Deformability and Convergence in the Higher-Order Numerical Manifold Method
    Kourepinis, D.
    Pearce, C. J.
    Bicanic, N.
    ANALYSIS OF DISCONTINUOUS DEFORMATION: NEW DEVELOPMENTS AND APPLICATIONS, 2010, : 283 - 290
  • [8] METHODS FOR REFINEMENT BY HIGHER-ORDER DIFFERENCES AND H2-EXTRA-POLATIONS
    VOLKOV, EA
    DOKLADY AKADEMII NAUK SSSR, 1963, 150 (03): : 455 - &
  • [9] CHAOS AND HIGHER-ORDER DIFFERENCES
    NEUBERGER, JW
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 101 (01) : 45 - 50
  • [10] On the convergence of higher-order orthogonal iteration
    Xu, Yangyang
    LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (11): : 2247 - 2265
12345