中文摘要：

对广义Improved KdV（GIKdV）方程的初边值问题提出了一种守恒的线性隐式差分格式,并利用能量分析方法证明了差分格式的稳定性和二阶收敛性。数值试验显示该格式是有效的。

英文摘要：

A new conservative linear-implicit difference scheme is presented for an initial-boundary value problem of the general Improved KdV（GIKdV） equation.It is proved by the discrete energy method that the scheme is unconditionally stable and second-order convergent.Numerical experiments demonstrate that the scheme is accurate and efficient.