ON THE CHOICE OF INITIAL CONDITIONS OF DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS

被引：0

作者：

Berikelashvili, G. ^{[1
,2
]}

Gupta, M. M. ^{[3
]}

Mirianashvili, M. ^{[4
]}

机构：

[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, 2 Univ Str, Tbilisi 0186, Georgia

[2] Georgian Tech Univ, Dept Math, Tbilisi 0175, Georgia

[3] George Washington Univ, Dept Math, Washington, DC 20052 USA

[4] N Muskhelishvili Inst Computat Math, Tbilisi 0193, Georgia

来源：

MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS | 2011年 / 53卷

关键词：

Heat equation; ADI difference scheme; high order convergence rate;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

when the exact solution belongs to the anisotropic Sobolev spaceWe consider the first initial-boundary value problem for linear heat conductivity equation with constant coefficient in Omega x (0, T], where Omega is a unit square. A high order accuracy ADI two level difference scheme is constructed on a 18-point stencil using Steklov averaging operators. We prove that the finite difference scheme converges in the discrete L2 -norm with the convergence rate O(h(s) + T-s/2), when the exact solution belongs to the anisotropic Sobolev space W-2(s,s/2) , s epsilon (2, 4].

引用

页码：29 / 38

页数：10

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