| 微分方程初值问题的GDQR解法 |
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| 引用本文： | 李志毅,陈殿云,雷旭升. 微分方程初值问题的GDQR解法[J]. 数值计算与计算机应用, 2005, 26(2): 135-140 |
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| 作者姓名： | 李志毅 陈殿云 雷旭升 |
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| 作者单位： | 河南科技大学 |
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| 基金项目： | 河南省科技攻关项目0424220224,0424220224． |
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| 摘 要： | 本文用最近由Wu提出的一种数值方法-GDQR(GeneralizedDifferentialQuadra-tureRule)对工程和科学技术中常遇到的2—4阶微分方程初值问题进行了求解.部分结果与精确解或龙格-库塔方法所得结果作了对比,表明GDQR在解决常微分方程初值问题时简单方便有效.
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| 关 键 词： | GDQR 微分方程 初值问题 欧拉方程 龙格-库塔方法 |
| 修稿时间： | 2002-08-09 |
INITIAL-VALUE EQUATIONS ANALYSIS BY THE GENERALIZED DIFFERENTIAL QUADRATURE RULE |
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| LI Zhiyi,Chen Dianyun,Lei Xusheng. INITIAL-VALUE EQUATIONS ANALYSIS BY THE GENERALIZED DIFFERENTIAL QUADRATURE RULE[J]. Journal on Numerical Methods and Computer Applications, 2005, 26(2): 135-140 |
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| Authors: | LI Zhiyi Chen Dianyun Lei Xusheng |
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| Abstract: | This paper introduces a new numerical method-Generalized Differential Quadrature Rule proposed by Wu in 2001. Using this method the authors solve several initial-value problems of differential equations of 2nd to 4nd order. Differential quadrature expressions are derived based on the GDQR for these equations. The numerical results were compared with the exact solutions and what obtained by using Runge-Kutta method. The numerical results indicate that GDQR has high efficiency and accuracy for initial-value problems of differential equations. |
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| Keywords: | GDQR differential equations initial-value Euler method Runge-Kutta method |
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