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

被引：0
|
作者：
V. G. Pimenov
A. B. Lozhnikov
机构：
[1] Ural Federal University,Institute of Mathematics and Mechanics
[2] Ural Branch of the Russian Academy of Sciences,undefined
[3] Ural Federal University,undefined
来源：
Proceedings of the Steklov Institute of Mathematics | 2011年 / 275卷
关键词：
numerical methods; heat conduction equation; delay; difference schemes; interpolation; extrapolation; order of convergence;
D O I：
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中图分类号：
学科分类号：
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.
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页码：137 / 148
页数：11
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