| 黄志龙,张丽强.用差分法与超松弛迭代法求高维平稳FPK方程的解[J].计算力学学报,2008,25(2):177~182 |
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| 用差分法与超松弛迭代法求高维平稳FPK方程的解 |
| Stationary solutions of high dimensional reduced FPK equation using both finite difference method and successive over-relaxation method |
| 修订日期：2006-03-26 |
| DOI：10.7511/jslx20082035 |
| 中文关键词: 差分法,超松弛迭代法,FPK方程 |
| 英文关键词:finite difference method,successive over-relaxation method,FPK equation |
| 基金项目:国家自然科学基金
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教育部跨世纪优秀人才培养计划 |
| 黄志龙 张丽强 |
| 浙江大学力学系 杭州310027 |
| 摘要点击次数: 1664 |
| 全文下载次数: 12 |
| 中文摘要: |
| 用不同精度的差分格式将高维平稳FPK方程离散化为线性代数方程组,然后用超松弛迭代法求解该线性代数方程组得到平稳FPK方程的近似解。讨论了不同的差分格式、网格密度及超松弛因子对解精度及收敛速度的影响,并与其他方法的计算精度进行比较,提出用多重网格算法提高计算效率。研究了典型的二维及四维随机系统的稳态响应,算例表明,该算法具有简洁、节省存储量且精度高的特点,是求解高维平稳FPK方程解的有效算法。 |
| 英文摘要: |
| The combination of finite difference method and successive over-relaxation method is employed to numerically get the stationary solution of high dimensional reduced Fokker-Planck-Kolmogorov(FPK)equation.The effects of different order of central difference scheme,the mesh density and factor of successive over-relaxation on the convergence and accuracy of numerical solution are discussed.A multi-mesh iterative method is proposed to improve the efficiency and accuracy of numerical solution.Two examples are given to illustrate the application of the proposed procedures. |
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