| 摘要: |
| 建立一种奇异摄动两点边值问题数值求解的高阶Hermite型有限体积法,给出该体积法的1个简单的计算格式,在较弱的条件下得到最佳阶的一致收敛性估计,并用数值实验验证该有限体积法的合理性和方法的有效性.结果表明,有限体积法和Galerkin方法几乎具有相同精度,最优收敛阶的实际值与理论值很接近. |
| 关键词: 奇异摄动问题 有限体积法 最优网格 |
| DOI： |
| 投稿时间：2009-10-25 |
| 基金项目:国家自然科学基金项目(10962001);广西自然科学基金资助项目(0575029)资助 |
|
| High Order Finite Volume Methods for the Second Order Singular Perturbation Problems |
|
HE Chong-nan
|
| (College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China) |
| Abstract: |
| A high order finite volume method of the Hermite type is established for solving the second order singular perturbation problems.A simple computing scheme of finite volume method is presented.The optimal order of uniform convergence is obtained under a much weaker condition than coercivity assumption.Numerical experiments are presented to verify our theoretical estimates.It shows that finite volume method and Galerkin method have nearly the same accuracy and the optimal order of uniform convergence calculated from the numerical errors is very closed to theoretical value. |
| Key words: singular perturbation problems finite volume method optimal meshes |
