对抛物型偏微分方程一种新的数值解法的研究  

The Study of a New Numerical Method for Parabolic Partial Differential Equations

作　　者：吐克孜.艾肯 阿布都热西提.阿布都外力 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2014年第1期64-69,共6页Journal of Xinjiang University(Natural Science Edition)

基　　金：塔克拉玛干沙漠扩散数学模型分析及其数值模拟(10971024)

摘　　要：根据抛物型偏微分方程数值解法的研究,对抛物型偏微分方程提出了新的数值解法.该方法在稳定性方面具有一定的优势,并具有计算简单,无条件稳定,误差小,编程方便等优点.证明了无条件稳定性,分析了相容性及收敛性,最后进行数值试验,验证了它的可行性.This paper proposed a new numerical method for Parabolic Partial Differential Equations ac-cording to the study of the numerical solution of parabolic equation. This method has certain advantages in terms of stability and has a simple calculation,unconditionally stable, the error is small, convenient program-ming.Verified the unconditional stability, theoretically analyzed the compatibility and convergence. Finally, correctness of it is verified with numerical experiments.

关 键 词：抛物型偏微分方程 Crank-Nicolson方法 稳定性 相容性 收敛性 

分 类 号：O241.82[理学—计算数学]