广义非线性Sine-Gordon方程的两个隐式差分格式

Two Implicit Difference Schemes for the Generalized Nonlinear Sine-Gordon Equation

本文对一类非线性Sine-Gordon方程的初边值问题提出了两个隐式差分格式．两个隐式差分格式的精度均为O(τ~2+h^2)．我们用离散泛函分析的方法证明了格式的收敛性和稳定性,并证明了求解格式的追赶迭代法的收敛性,最后给出了数值结果．结果表明本文的格式是有效的和可靠的．

In this paper, a implicit scheme and a compact scheme for the solution of an initial-boundary value problem of the generalized nonlinear Sine-Gordon Equation are presented. The trunction error of the two schemes is O（τ^2＋h2）.The convergence and stability are obtained by the discrete functions analysis method. At last, we give the numerical results of the two schemes. The numerical experments demonstrate that our algorithms are effective and reliable.