| 一类变系数微分方程差分格式的收敛性(英文) |
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| 引用本文： | 徐琛梅,菅帅,王波. 一类变系数微分方程差分格式的收敛性(英文)[J]. 应用数学, 2012, 25(3): 570-576 |
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| 作者姓名： | 徐琛梅 菅帅 王波 |
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| 作者单位： | 1. 河南大学数学与信息科学学院,河南开封,475001
2. 中国科学院数学与系统科学学院,北京,100080 |
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| 基金项目： | Supported by the Natural Science Foundation of the Education Department of Henan Province(2010A100003);the National Natural Science Foundation of China(40805020) |
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| 摘 要： | 本文首先对一类变系数微分方程建立有限差分格式.然后利用矩阵的特征值和范数理论,讨论该格式解的收敛性和唯一性.通过数值算例,说明该格式既有效又便于模拟.并且文中所用方法还能用于高阶微分方程和某些非线性微分方程问题的研究.
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| 关 键 词： | 收敛性 差分格式 变系数微分方程 总体截断误差 |
Convergence of the Difference Scheme for a Class Differential Equations with Variable Coefficients |
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| XU Chenmei , JIAN Shuai , WANG Bo. Convergence of the Difference Scheme for a Class Differential Equations with Variable Coefficients[J]. Mathematica Applicata, 2012, 25(3): 570-576 |
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| Authors: | XU Chenmei JIAN Shuai WANG Bo |
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| Affiliation: | 1 (1.College of Mathematics and Information Science,Henan University,Kaifeng 475001,China;2.Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China) |
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| Abstract: | In this paper,the finite difference scheme for a class differential equations with variable coefficients is presented.The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalue and norm.The numerical example shows that the scheme is very simple to implement and efficient.This method can be applied to the study of higher-order and some nonlinear differential equations problems. |
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| Keywords: | Convergence Difference scheme Differential equation with variable coefficient Total truncation error |
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