非线性Leland方程的交替分组显式迭代方法

Alternating group explicit iterative method for nonlinear Leland equation

将隐式差分方程组在每一时间层上划分为若干子方程组来同时进行迭代求解,给出非线性Leland方程的一类AGEI格式。理论分析表明:基于经典Crank-Nicolson(C-N)格式构造的AGEI-CN格式具有二阶精度,格式解存在唯一且收敛。数值试验显示:AGEI-CN格式的计算时间比经典C-N格式节省近69%,比交替分组C-N(ASC-N)格式节省近36%,表明本文提出的AGEI方法对于求解非线性Leland方程是有效的。

The implicit difference equations are divided into several sub equations at each time layer to solve them simultaneously,and a class of AGEI schemes for nonlinear Leland equations is given.Theoretical analysis shows that alternating group explicit iterative Crank-Nicolson（AGEI-CN）based on classical Crank-Nicolson（C-N）has second accuracy,and the form solution is unique and convergent.Numerical experiments show that AGEI-CN scheme saves 69 percent of time with contrast to C-N and saves 36 percent of time with contrast to ASC-N,indicating that the method proposed by this paper can solve nonlinear Leland equation effectively.