解KdV方程的一个隐式差分格式

AN IMPLICIT DIFFERENCE SCHEME FOR KdV EQUATION

对ＫｄＶ方程ｕ＿ｔ＋ｕｕ＿ｚ＋Ｅｕ＿（ｚｚｚ）＝０构造了一个二层隐式差分格式，具有三对角线阵，其局部截断误差为Ｏ（τ＋ｈ＋τ／ｈ），其线性化稳定条件为（１＋２ＬＱ）￣２≥１，Ｌ＝τ／ｈ，数值例子表明，格式长时间稳定，可以描述孤波（Ｓｏｌｉｔｏｎ）的性态．

A two -level implicit difference scheme for KdV equation u_i+uu_z+Eu_(zzz)=0 is established. Its local truncation error is O(τ+h+τ/h)and linearization stabiliy condition is(1+2LQ)￣2≥1(L=τ/h, The scheme corresponds a system of linearequations with tridiagonal matrix ,which can be solved by double sweep method if boundary values aregiven. The numerical example shows that the scheme has long time stability and can be used to describethe behaviour of soliton.