| 一类非线性发展方程的特征中心差分法 |
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| 引用本文： | 郭双冰,张志跃. 一类非线性发展方程的特征中心差分法[J]. 计算物理, 2007, 24(6): 637-646 |
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| 作者姓名： | 郭双冰 张志跃 |
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| 作者单位： | 南京师范大学效学与计算机科学学院,江苏,南京,210097;南京师范大学效学与计算机科学学院,江苏,南京,210097 |
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| 基金项目： | 国家自然科学基金 , 江苏省教育厅科研项目 , 江苏省海外留学基金 , 江苏省科技厅科研项目 |
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| 摘 要： | 给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度ut及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,ut对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性.
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| 关 键 词： | 非线性发展方程 特征中心差分法 误差估计 |
| 文章编号： | 1001-246X（2007）06-0637-10 |
| 收稿时间： | 2006-07-03 |
| 修稿时间： | 2006-12-28 |
Numerical Methods Based on Characteristic Centered Finite Difference Procedure for a Class of Nonlinear Evolution Equations |
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| GUO Shuangbing,ZHANG Zhiyue. Numerical Methods Based on Characteristic Centered Finite Difference Procedure for a Class of Nonlinear Evolution Equations[J]. Chinese Journal of Computational Physics, 2007, 24(6): 637-646 |
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| Authors: | GUO Shuangbing ZHANG Zhiyue |
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| Affiliation: | School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China |
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| Abstract: | We propose a characteristic centered difference method for a class of nonlinear evolution equations on nonregular grids.Approximate solution and error estimate of u,u_t,u_x,u_(tx) are obtained.The compuational load of the method is the same as those of the characteristic difference method based on linear interpolation.And the error order of the approximate solution is the same as one of the characteristic difference method based on quadratic interpolation.Moreover,the first derivative of u,u_t in space shows super-covergent order error estimate.Numerical results demonstrate feasibility and efficiency of the methods. |
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| Keywords: | nonlinear evolution equation characteristic centered finite difference method error estimate |
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