|
| 摘要: |
| 本文首先构造了分数阶拉普拉斯算子的一种新型积分公式，并给出了相应的误差估计.基于该积分公式，我们设计了一种求解分数阶拉普拉斯方程的新型有限差分格式，并得到了该格式的最优误差分析.最后通过一些数值实验验证了格式的高效性和理论分析的正确性. |
| 关键词: 分数阶拉普拉斯方程 有限差分方法 数值积分公式 误差分析 |
| DOI： |
| 分类号:O241.8 |
| 基金项目: |
|
| A NEW FINITE DIFFERENCE METHOD FOR SOLVING FRACTIONAL LAPLACIAN EQUATION |
|
WANG Jing,ZHANG Xiao-ping
|
| Abstract: |
| In this paper, we first propose a new quadrature rule for evaluating the fractional Lapalcian operator, and the corresponding error estimate is derived. Based on this quadrature rule, we design a new finite difference method for solving fractional Laplacian equation, while the optimal convergence analysis is obtained. Finally, some numerical tests are provided to validate the effetiveness of the scheme and the correctess of the theorectical analysis. |
| Key words: Fractional Laplacian quadrature rule finite difference error estimate |
