微分方程初值问题的数值解法的比较
he compare of Numerical Solution Research of Initial Value Problem of Differential Equation
本文主要讨论了满足某种初值问题的微分方程的数值解法。把数值解法分为单步法和多步法两种, 并列举了常用的单步法: 如欧拉法、龙格-库塔法, 以及常用的多步法: 如阿当姆斯显式法、阿当姆斯隐式法、预测-校正格式。最后通过实例对多种微分方程初值问题的数值解法的精度进行了比较, 从而得到应根据问题的不同形式来选择算法。
In this paper, it discusses the numerical solution of differential equation which is needed to meet certain initial conditions. The numerical solution divides one-step and multi-step, and it enumertes one-step which is often used such as: Euler、Runge-Kutta, and multi-step which is often used such as: Admas-Bashforth、Adams-Monlton、PECE. At last, it compare a variety of numerical solution of initial value problem in terms of accuracy, and obtain that we should choose solution towards different form of differential equation.
任亮、崔恩华、孙坤、谭玲、刘礼昱
数学
微分方程初值问题数值解法误差
ifferential equationInitial value problemNumerical solutionError
任亮,崔恩华,孙坤,谭玲,刘礼昱.微分方程初值问题的数值解法的比较[EB/OL].(2010-07-20)[2025-08-10].http://www.paper.edu.cn/releasepaper/content/201007-367.点此复制
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