Difference schemes for the numerical solution of the heat conduction equation with aftereffect

被引：17

作者：

Pimenov, V. G. ^{[1
]}

Lozhnikov, A. B. ^{[2
,3
]}

机构：

[1] Ural Fed Univ, Ekaterinburg 620002, Russia

[2] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620990, Russia

[3] Ural Fed Univ, Ekaterinburg 620002, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2011年 / 275卷

基金：

俄罗斯基础研究基金会;

关键词：

numerical methods; heat conduction equation; delay; difference schemes; interpolation; extrapolation; order of convergence;

D O I：

10.1134/S0081543811090100

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A family of grid methods is constructed for the numerical solution of the heat conduction equation in the general form with delay; the methods are based on the idea of separating the current state and the prehistory function. A theorem is obtained on the order of convergence of the methods, which uses the technique of proving similar statements for functional differential equations and methods from the general theory of difference schemes. Results of calculating test examples with constant and variable delay are presented.

引用

页码：137 / 148

页数：12

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