一类时滞抛物型方程的差分格式

A Difference Scheme for a Class of Delay Parabolic Equations

对一般的带有初边值问题的时滞抛物型方程建立了1个Crank-Nicolson型差分格式。用离散能量法证明了该差分格式解的存在唯一性和收敛性,其收敛阶数为o(τ~2+h^2),并用仿真结果验证了相关结论。

A Crank-Nicolson scheme is established for a general delay parabolic equation with the initial bounda- ry value problem. It is proved that the solution of the difference scheme is existence, uniqueness and conver- gence using the discrete energy method. The convergence order is o（r^2 ＋ h^2） in L∞^ norm. Finally, a numerical example is provided to testify the results.