Method of corrections by higher order differences for Poisson equation with nonlocal boundary conditions

被引：0
|
作者：
Berikelashvili, Givi [1 ,2 ]
Midodashvili, Bidzina [3 ,4 ]
机构：
[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, 6 Tamarashvili St, GE-0177 Tbilisi, Georgia
[2] Georgian Tech Univ, Dept Math, 77 M Kostava Str, GE-0175 Tbilisi, Georgia
[3] I Javakhishvili Tbilisi State Univ, Fac Exact & Nat Sci, 2 Univ Str, GE-0186 Tbilisi, Georgia
[4] Gori Teaching Univ, Fac Educ Exact & Nat Sci, 5 I Chavchavadze Str, Gori, Georgia
来源：
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2016年 / 170卷 / 02期
基金：
美国国家科学基金会;
关键词：
Nonlocal BVP; Difference scheme; Method of corrections; Improvement of accuracy; Compatible estimates of convergence rate;
D O I：
10.1016/j.trmi.2016.04.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Bitsadze-Samarskii type nonlocal boundary value problem for Poisson equation in a unit square, which is solved by a difference scheme of second-order accuracy. Using this approximate solution, we correct the right-hand side of the difference scheme. It is shown that the solution of the corrected scheme converges at the rate O(|h|(s)) in the discrete L-2-norm provided that the solution of the original problem belongs to the Sobolev space with exponent s epsilon [2, 4]. (C) 2016 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.
引用
收藏
页码：287 / 296
页数：10
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