含阻尼项的SRLW方程的一个去耦合线性化差分格式

本文对带有阻尼项的耗散SRLW方程的初边值问题进行了数值方法研究，提出了一个具有二阶理论精度的三层非耦合线性化差分格式，由于该格式解除了原方程中函数 和 的耦合关系，数值求解时只需对函数 和 分别单独求解，其中对函数 的数值求解为线性化差分算法，对函数 的数值求解为显式差分算法直接求解，从而大大提高了数值求解效率。在不能得到其差分解最大模估计的情况下，综合运用数学归纳法和离散泛函分析方法，直接证明了格式的收敛性和稳定性。数值实验表明该方法是可靠的.

A decoupled linearized difference scheme for the SRLW equation with damping term

In this paper, a numerical method of initial-boundary value problem for the dissipative SRLW equation with damping term is considered. A three-level uncoupled linearized difference scheme with the second order accuracy is proposed, because the scheme removes the coupling relationship between and ,we can solve the functions and respectively. Here, is solved by a linearized difference algorithm for numerical solution and is directly solved by the explicit difference algorithm, so this scheme greatly improves the numerical solution efficiency. In the case that the maximum modulus estimation of the difference solution fails to be obtained, convergence and stability of numerical solutions are proved directly by inductive method and discrete functional analysis. Finally, the efficiency of the method is demonstrated by numerical examples.