| 摘要: |
| 针对对流方程第一类初边值问题,基于子域精细积分的思想,结合三次样条函数逼近,提出一个含参数T(T>0)无条件稳定的样条子域精细积分(SSPI)格式,并进行数值实验.SSPI格式求解对流方程有效,而且局部截断误差为O(Tf2+f2+h4).SSPI格式不仅能够求解对流方程的第一类边值问题,而且能够求解第二类、第三类初边值问题,是一种有效的算法. |
| 关键词: 对流方程 三次样条函数 子域精细积分 稳定性 |
| DOI： |
| 投稿时间：2007-12-10 |
| 基金项目:广西自然科学基金项目(0575029,0639008);广西研究生教育创新计划项目(2006106080701M10);广西民族大学研究生教育创新基金项目(GXUN-CHX0756)资助 |
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| Spline Sub-domain Precise Integration Scheme for Solving Convection Equation |
|
LIU Li-bin, LIU Huan-wen
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| (College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China) |
| Abstract: |
| Based on sub-domain precise integration method and combined the cubic spline function approximation, it presents the Spline Sub-domain Precise Integration (SSPI)scheme containing parameter for the first initial-boundary value problem of convection equation.It is showed that this implicit scheme is unconditionally stable.The accuracy of the SSPI method is O (Tf2+f2+h2), and the present method can be conveniently used to solve the second and the third initial-boundary value problems, it is a effective method. |
| Key words: convection equation cubic spline function sub-domain precise integration stability |
