一类半线性抛物型方程的紧差分格式  

A Compact Difference Scheme for a Class of Semilinear Parabolic Equations

作　　者：吴宏伟[1] 

机构地区：[1]东南大学数学系,江苏南京210096

出　　处：《应用数学》2007年第2期421-426,共6页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10471023)

摘　　要：本文构造了一类半线性抛物方程初边值问题的紧差分格式.利用离散能量估计证明了差分格式解的存在唯一性、收敛性和无条件稳定性,并给出了在离散L∞模意义下收敛阶数为O(h4+τ2).数值例子验证了理论分析结果.In this paper, a linearized two-level compact finite difference scheme is presented for a class of semilinear parabolic equations. Existence and uniqueness of the difference solution are proved. It is also shown that the solution of compact difference scheme is convergent and unconditional stable in discrete norm L^∞ and the convergence order is O（h^4＋τ^2）. In addition, a numerical experiment illustrates the results of the presented method.

关 键 词：半线性抛物方程 紧差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]