Application of the Maximum Principle for Differential Equations in Combination with the Finite Difference Method to Find Transient Approximate Solutions of Heat Equations and Error Analysis
Application of the Maximum Principle for Differential Equations in Combination with the Finite Difference Method to Find Transient Approximate Solutions of Heat Equations and Error Analysis
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DOI：
10.1080/10407790802557524
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发表时间：
2009-01
期刊：
影响因子：
--
通讯作者：
Chi-Chang Wang
中科院分区：
文献类型：
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作者：
Chi-Chang Wang
本文试图将微分方程的极大值原理与有限差分法相结合。有限差分法已被广泛用于求瞬态热传导问题精确解的上解和下解。通过实例验证，本文所提出的方法能够利用有限差分法正确求得精确解的上下近似解，而有限差分法原来不适用于微分方程的极大值原理。用这种方法得到的上下近似解不仅可以指示精确解存在的范围，而且可以用来进一步分析在最不利条件下平均近似解与未知精确解之间的误差。
This article tries to combine the maximum principle for differential equations with the finite-difference method that has been widely used to find upper and lower solutions of the exact solutions of transient heat conduction problems. As verified by some examples, the technique proposed in this article is successful in obtaining lower and upper approximate solutions of the exact solution correctly by using the finite-difference method, which originally does not apply to the maximum principle for differential equations. The lower and upper approximate solutions obtained with such a method not only can indicate the range where the exact solutions exist, but also can be used to further analyze the error between mean approximate solutions and unknown exact solutions under the most unfavorable condition.