全文总字数：5628字

1. 研究目的与意义及国内外研究现状

有限差分方法是求解微分方程重要而有效的数值手段。

近年来,随着人们对微分方程数值方法研究的深入,高精度的有限差分方法日益受到人们的重视,紧致差分格式就是一类高精度的有限差分方法。

它具有精度高,分辨率高,对网格节点数要求不高等优点,因而受到很多学者的关注。

2. 研究的基本内容

1. 给出KGS方程的一个紧致差分格式，并证明其满足两个守恒率；
2. 进行误差分析；
3. 进行一些数值实验，验证格式的准确性和应用性。

3. 实施方案、进度安排及预期效果

2017年2月之前：学习毕业论文有关文件，认真填写任务书，确定好题目。

2017年3月：完成任务书、开题报告、外文翻译。

2017年4月：撰写论文初稿，并交导师审核。

4. 参考文献

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