一类半线性抛物方程的差分格式及收敛性和稳定性  

Convergence and Stability of a Difference Scheme for Some Semilinear Parabolic Equations

作　　者：吴宏伟[1] 

机构地区：[1]东南大学数学系,南京210096

出　　处：《工程数学学报》2008年第3期551-554,共4页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10471023).

摘　　要：本文讨论一类半线性抛物方程初边值问题的线性化二层隐式差分格式,证明了差分格式的可解性、收敛性和无条件稳定性,并指出了在离散L2模和L∞模意义下的收敛阶数为O(h2+τ2)。数值例子验证了理论分析结果。In this paper, a linearized two-level finite difference scheme is designed for semilinear parabolic equations. Existence and uniqueness of the difference solution are proved, We also established convergence and unconditional stability of the difference scheme in discrete norm L^2 and L^∞, respectively. In addition, it is shown that the convergence order of difference scheme is O（h^2 ＋ τ^2） in both discrete norm L^2 and L^∞, respectively. A numerical experiment for semilinear parabolic equations is also given.

关 键 词：半线性抛物方程 有限差分格式 收敛性 稳定性 

分 类 号：O175.26[理学—数学] O241.82[理学—基础数学]