摘要
通过分析步长与数值误差的关系,论证了调整和优化步长的必要性。从步长与误差的关系出发,介绍了数值求解初值微分方程问题的两种优化步长的方法:两步计算法和嵌入式龙格-库塔法。在用隐式欧拉法对反应堆点动态学方程进行数值求解时,采用两步计算法对步长进行优化,计算的结果表明控制误差对步长及数值解的精确性有决定性的影响;通过求解反应堆点动态学方程,对MATLAB自带的嵌入式龙格-库塔法的微分方程求解函数ode23及ode45的精确性及使用情况进行了探讨。
Based on the analysis of effects of time step-size on numerical solutions, this paper showed the necessity of step-size adaptation. Based on the relationship between error and step-size, two-step adaptation methods for solving initial value problems （IVPs） were introduced. They are Two-Step Method and Embedded Runge-Kutta Method. PRKEs were solved by implicit Euler method with step-sizes optimized by using Two-Step Method. It was observed that the control error has important influence on the step-size and the accuracy of solutions. With suitable control errors, the solutions of PRKEs computed by the above mentioned method are accurate reasonably. The accuracy and usage of MATLAB built-in ODE solvers ode23 and ode45, both of which adopt Runge-Kutta-Fehlberg method, were also studied and discussed.
出处
《核动力工程》
EI
CAS
CSCD
北大核心
2007年第2期8-12,共5页
Nuclear Power Engineering
