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求解广义正则长波方程的守恒差分格式
A Conservative Finite Difference Scheme for Generalized Regularized Long-wave Equation
【摘要】 本文对广义正则长波方程的初边值问题提出了—个隐式差分格式,该格式合理地模拟了方程本身所具有的两个守恒律.给出了差分解的先验估计,证明了差分解的唯一可解性、无条件收敛性及其稳定性.
【Abstract】 In this paper, an, implicit finite difference scheme is constructed for the initial-boundary value problem of a generalized Regularized Long-Wave equation. The scheme has the advantages that it preserves some invariant properties of the original differential equation. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable and second order convergent in l∞norm on the basis of the priori estimates.
【关键词】 广义正则长波方程;
有限差分格式;
守恒性;
唯一可解性;
收敛性;
稳定性;
【Key words】 generalized Regularized Long-Wave equation; finite difference scheme; conservation; unique solvablity; convergence; stability;
【Key words】 generalized Regularized Long-Wave equation; finite difference scheme; conservation; unique solvablity; convergence; stability;
【基金】 国家自然科学基金(10471023,10572057)资助项目.
- 【文献出处】 应用数学学报 ,Acta Mathematicae Applicatae Sinica , 编辑部邮箱 ,2006年06期
- 【分类号】O241.82
- 【被引频次】24
- 【下载频次】159