| 半线性椭圆方程的一个新的双重网格差分算法 |
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| 引用本文： | 刘伟,王智峰.半线性椭圆方程的一个新的双重网格差分算法[J].山东大学学报(理学版),2005,40(6):39-43,61. |
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| 作者姓名： | 刘伟 王智峰 |
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| 作者单位： | 1. 山东大学,数学与系统科学学院,山东,济南,250100
2. 烟台大学,数学与信息科学系,山东,烟台,264005 |
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| 基金项目： | 国家自然科学基金资助项目（10471079） |
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| 摘 要： | 用所提出的双重网格算法研究了半线性椭圆方程，其对粗网格（可以很粗）的非线性解在细网格上进行了几次线性修正．无需求解细网格上的非线性解，且重复算法最后两步，可使解的误差估计达到任意阶精度，并提出了相应的数值算例．
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| 关 键 词： | 双重网格法 非线性椭圆方程 有限差分法 |
| 文章编号： | 1671-9352（2005）06-0039-05 |
| 收稿时间： | 2004-12-10 |
| 修稿时间： | 2004-12-10 |
A novel two-grid difference algorithm for semilinear elliptic equations |
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| LIU Wei,WANG Zhi-feng.A novel two-grid difference algorithm for semilinear elliptic equations[J].Journal of Shandong University,2005,40(6):39-43,61. |
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| Authors: | LIU Wei WANG Zhi-feng |
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| Institution: | 1. School of Math. and System Sci., Shangdong Univ., Jinan 250100, Shandong, China; 2. Department of Mathematics and Information Science, Yantai Univ., Yantai 264005, Shandong, China |
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| Abstract: | A novel algorithm based on two grid difference method is presented.Three linear corrections on fine grid for the nonli-(near) solution on coarse grid(it can be extremely coarse) are performed.It's unnecessary to get the nonlinear solution on fine grid and any-order accuracy is obtained for error estimate of solution by repeating the last two steps of this algorithm.The numerical results validating the theory are also presented. |
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| Keywords: | two-grid method nonlinear elliptic equations finite difference method |
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