热传导方程的Crank-Nicolson差分解在边界附近的变化研究  

Dispose of Variability of the Crank-Nicolson Solution of Heat Equation near the Boundaries

作　　者：娜扎开提·阿迪力 伊马木·麦麦提 阿布都热西提·阿布都外力 Nazakat Adil Imam Mamat Abdirixit Abduwali

出　　处：《新疆大学学报（自然科学维文版）》2017年第1期16-22,共7页JOURNAL OF XINJIANG UNIVERSITY

摘　　要：用Crank-Nicolson格式求热传导方程第一类初边值问题的近似解时，发现绝对稳定的Crank-Nicolson格式在边界附近出现振动。本文中讨论了振动的发生原因及提出了控制振动的一种方法，并通过数值实验分析了该方法的可行性，得到了较好的结果。In this paper, the effects of different initial and boundary condition to the numerical solutions were discussed. Some oscillations near point of discontinuity on both the initial and boundary condition were found by using the unconditionally stable Crank-Nicolson scheme. Then the reasons of oscillations and new method to control the oscillations were laid out. With results of numerical experiments, we analyzed the error of the method.

关 键 词：热传导方程 CRANK-NICOLSON格式 插值多项式 

分 类 号：O551.3[理学—热学与物质分子运动论]