三维热传导方程的修正局部C-N方法  

Modified local Crank-Nicolson method for solving three dimensional heat conduction equations

作　　者：周文格[1] 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：《山东理工大学学报（自然科学版）》2015年第1期10-14,共5页Journal of Shandong University of Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(10971024)

摘　　要：对三维热传导方程的经典Crank-Nicolson格式运用指数函数的Trotter Product公式进行修正和改进,推出一种求解三维热传导方程的修正局部Crank-Nicolson方法,该方法具有计算量小和精度高的优点.证明了修正局部Crank-Nicolson格式的无条件稳定性和收敛性,最后用数值实验验证了该方法的准确性和有效性.The classical Crank-Nicolson scheme of three-dimensional heat conduction equations is modified and improved,using Trotter Product formula of the exponential function.The modified local Crank-Nicolson method is developed for solving three-dimensional heat conduction equation,and it has the characteristics of a small amount of calculation and high precision.We also proved unconditional stability and convergence of the modified local Crank-Nicolson method.Finally the numerical experiment is conducted to verify the accuracy and availability of the method.

关 键 词：三维热传导方程 Trotter Product公式 修正局部Crank-Nicolson方法 稳定性和收敛性. 

分 类 号：O193[理学—数学]