二维半线性抛物方程的二重网格差分算法  

Two-grid Difference Algorithms for Two-dimensional Semilinear Parabolic Equation

作　　者：刘伟[1] 芮洪兴[2] 刘春玲[1] 

机构地区：[1]鲁东大学数学与信息学院,烟台264025 [2]山东大学数学与系统科学学院,济南250100

出　　处：《工程数学学报》2007年第5期885-889,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10471079);教育部博士点基金(20060422006).

摘　　要：针对二维半线性抛物方程,本文提出了两种二重网格差分算法,并给出了误差估计。该算法能够在粗网格和细网格上线性地求解半线性问题。若重复算法的最后几步可以按粗网格步长任意阶地逼近细网格上的非线性解。Two efficient methods with two-grid scheme are presented in this paper for the approximation of semilinear parabolic equations by using the finite difference method. The proposed techniques are based on two different spaces defined, respectively, on a coarse grid and a fine grid. By the two-grid algorithms, the semilinear parabolic problem is solved by the linear method without sacrificing the order of accuracy of the fine grid solution. A remarkable fact is that any order accuracy of approximation in coarse grid size can be obtained if other iterations are performed similarly to final steps of the algorithms.

关 键 词：有限差分法 半线性抛物方程 二重网格法 

分 类 号：O241.3[理学—计算数学]