基于不同分裂的修正局部Crank-Nicolson方法对一维热传导方程的应用  

Application of the Modified Local Crank-Nicolson Method for Solving the one-dimensional heat Equation based on the different division

作　　者：郭瑞[1] 阿布都热西提.阿布都外力 

机构地区：[1]石河子大学理学院,新疆石河子832003 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《兵团教育学院学报》2011年第2期75-78,84,共5页Journal of Bingtuan Education Institute

基　　金：新疆高校科研计划资助项目(XJEDU2007I02);国家自然科学基金(10961024)

摘　　要：本文采用不同分裂的修正局部Crank-Nicolson方法讨论了一维热传导方程的初边值问题。该方法不仅具有原来计算量少,无条件稳定的优点,而且推广了该方法对复杂的数学物理方程应用的可能性。理论上分析了无条件稳定性、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 uses the modified local Crank - Nicolson method to solve the one - dimensional initial - boundary value problem of heat equation based on different divisions. This method not only has the advantage of little calculation and unconditional stability, but also develops the method to be used to solve more complicate equations of mathematical physics. Unconditional stability, compatibility and convergence are discussed in theoretical. Finally, verify correctness of it with numerical experiments.

关 键 词：不同分裂的修正局部Crank-Nicolson法 无条件稳定性 相容性 收敛性 热传导方程. 

分 类 号：O241.82[理学—计算数学]