A nonstandard finite difference scheme for nonlinear heat transfer in a thin finite rod

被引：33

作者：

Jordan, PM ^{[1
]}

机构：

[1] USN, Res Lab, Stennis Space Ctr, MS 39529 USA

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2003年 / 9卷 / 11期

关键词：

Stefan-Boltzmann radiation law; nonstandard finite difference scheme; diffusion equation; positivity;

D O I：

10.1080/1023619031000146922

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonstandard finite difference scheme is constructed to solve an initial-boundary value problem involving a quartic nonlinearity that arises in heat transfer involving conduction with thermal radiation. It is noted that the positivity condition is equivalent to the usual linear stability criteria and it is shown that the representation of the nonlinear term in the finite difference scheme, in addition to the magnitudes of the equation parameters, has a direct bearing on the scheme's stability. Finally, solution profiles are plotted and avenues of further inquiry are discussed.

引用

页码：1015 / 1021

页数：7

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[2]

Burmeister L., 1993, CONVECTIVE HEAT TRAN

[3]

Carslaw H. S., 1959, CONDUCTION HEAT SOLI

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