Numerical methods for ordinary differential equations in the 20th century
Numerical methods for ordinary differential equations in the 20th century
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DOI：
10.1016/s0377-0427(00)00455-6
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发表时间：
2000-12-15
影响因子：
2.4
通讯作者：
Butcher, JC
中科院分区：
文献类型：
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作者：
Butcher, JC
由于多种原因，求解常微分方程初值问题的数值方法在 20 世纪取得了巨大进步。第一个原因在于上个世纪末 Bashforth 和 Adams 的线性多步方法和 Runge 的 Runge-Kutta 方法的开创性论文对这一主题的推动。其他原因当然也适用于一般的数值分析，包括本世纪中叶电子计算机的发明以及对高效数值算法的数学建模的需求，以替代应用数学的经典方法。这篇综述论文跟踪了这些方法发展的许多主要趋势，包括一般问题、刚性系统，以及许多随着本世纪末而变得越来越重要的特殊问题类型。 (C) 2000 Elsevier Science B.V. 保留所有权利。
Numerical methods for the solution of initial value problems in ordinary differential equations made enormous progress during the 20th century for several reasons. The first reasons lie in the impetus that was given to the subject in the concluding years of the previous century by the seminal papers of Bashforth and Adams for linear multistep methods and Runge for Runge-Kutta methods. Other reasons, which of course apply to numerical analysis in general, are in the invention of electronic computers half way through the century and the needs in mathematical modelling of efficient numerical algorithms as an alternative to classical methods of applied mathematics. This survey paper follows many of the main strands in the developments of these methods, both for general problems, stiff systems, and for many of the special problem types that have been gaining in significance as the century draws to an end. (C) 2000 Elsevier Science B.V. All rights reserved.