期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Nonstandard Finite Difference Schemes for a KdV Equation
摘要/Abstract
摘要：
给出了一类KdV方程的精确差分格式和非标准有限差分格式.先构造KdV方程的精确有限差分格式，并由此推导出一个非标准有限差分格式.在构造差分格式中，重点给出步长函数（分母函数）的具体形式，同时证明了该方法可以保持KdV方程解的正性和有界性.通过数值实验验证了非标准有限差分格式的可行性和有效性.
Abstract：
In this paper,we give an accurate difference scheme and nonstandard finite difference scheme for a class of KdV equation.The exact finite difference scheme of the KdV equation is constructed and a nonstandard finite difference scheme is derived.In the construction of the difference scheme,the concrete form of the step function (denominator function) is given,and it is proved that thise method keeps the positivity and boundedness of the solution of the KdV equation.The feasibility and validity of the nonstandard finite difference scheme are verified by numerical experiments.
关键词
Key words：
exact finite difference
;
nonstandard finite difference
;
KdV equation
;
positivity
参考文献 16
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