| 一类偏积分微分方程二阶差分全离散格式 |
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| 引用本文： | 陈红斌,陈传淼,徐大.一类偏积分微分方程二阶差分全离散格式[J].计算数学,2006,28(2):141-154. |
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| 作者姓名： | 陈红斌 陈传淼 徐大 |
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| 作者单位： | 1. 中南林业科技大学理学院数学教研室,长沙,410004
2. 湖南师范大学数学与计算机科学学院,长沙,410081 |
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| 基金项目： | 中国科学院资助项目;中南林业科技大学校科研和校改项目 |
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| 摘 要： | 本文给出了数值求解一类偏积分微分方程的二阶差分全离散格式．时间方向采用了二阶向后差分格式,积分项的离散利用了Lubich的二阶卷积求积公式,给出了稳定性的证明、误差估计及收敛性的结果,并给出了数值例子．
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| 关 键 词： | 偏积分微分方程 分数次计算 卷积求积 差分格式 二阶全离散 |
| 收稿时间： | 2004-11-24 |
| 修稿时间： | 2004-11-24 |
A SECOND ORDER FULLY DISCRETE DIFFERENCE SCHEME FOR A PARTIAL INTEGRO-DIFFERENTIAL EQUATION |
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| Chen Hongbin,Chen Chuanmiao,Xu Da.A SECOND ORDER FULLY DISCRETE DIFFERENCE SCHEME FOR A PARTIAL INTEGRO-DIFFERENTIAL EQUATION[J].Mathematica Numerica Sinica,2006,28(2):141-154. |
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| Authors: | Chen Hongbin Chen Chuanmiao Xu Da |
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| Institution: | Chen Hongbin (Faculty room for Mathematics, College of Science, Central South University of Forestry & Technology, Changsha, 410004, China) Chen Chuanmiao Xu Da (College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, China) |
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| Abstract: | In this paper, the second order fully discrete difference method for a partial integro-differential equation is considered. Second order backward difference scheme is empolied in time; The integral term is treated by means of the second order convolution quadrature suggested by Lubich; The stability, error estimate is given; Numerical experiments are reported. |
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| Keywords: | partial integro-differential equation fractional calculus convolution quadrature finite difference scheme second order fully discrete |
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