常微分方程初值问题的高阶泰勒法与龙格-库塔法之应用对比  

Application comparisons of higher order Taylor method and Runge-Kutta method for initial value problem of ordinary differentiable equations

作　　者：江山[1] 张岩 孙美玲[2] JIANG Shan;ZHANG Yan;SUN Mei-ling(School of Science,Nantong University,Nantong 226019,China;Department of Public Courses,Nantong Vocational University,Nantong 226007,China)

机构地区：[1]南通大学理学院,江苏南通226019 [2]南通职业大学公共教学部,江苏南通226007

出　　处：《高师理科学刊》2019年第12期12-15,共4页Journal of Science of Teachers＇College and University

基　　金：江苏省高校青蓝工程优秀青年骨干教师资助项目;南通大学教学改革研究课题（2018B06）

摘　　要：常微分方程的初值问题有着广泛应用,其数值解的精确化和高效化一直是人们追求的目标.基于严谨数学理论提升局部截断误差的阶数,从而达到提升整体截断误差阶数的目的,给出高阶泰勒法与龙格-库塔法的迭代公式.通过具体算例,比较各种高阶算法的计算精度和计算效率,给出对应的数值误差与图表说明,充分验证2类高阶方法各自的优势与缺陷,为求解实际应用问题提供参考依据.The initial value problem of ordinary differentiable equation is universally used,its most accurate and most efficient numerical solution is always a goal.Based on mathematical theories to upgrade the order of local truncation error,consequently the order of global truncation error is upgraded too,the higher-order Taylor and Runge-Kutta iterative formula are presented.The computational accuracy and efficiency from different algorithms are compared through numerical experiments,and their corresponding errors are plotted and listed.In this way,sufficiently validates the advantages and disadvantages of these higher-order methods,and provides references for solving practical application problems.

关 键 词：常微分方程 初值问题 泰勒法 龙格-库塔法 

分 类 号：O241.81[理学—计算数学]