一维微分方程的多项式特解方法  

The Method of Polynomial Particular Solutions for Solving Ordinary Differential Equations

作　　者：曹艳华 李楠 张姊同 陈清详 罗文俊 郑辉 CAO Yanhua;LI Nan;ZHANG Zitong;CHEN Qingxiang;LUO Wenjun;ZHENG Hui(School of Sciences,East China Jiaotong University,Nanchang 330013,China;School of Mathematics and Natural Sciences,University of Southern Mississippi,U.S.A.;School of Civil Engineering and Architecture,Nanchang University,Nanchang 330000,China)

机构地区：[1]华东交通大学理学院,江西南昌330013 [2]南密西西比大学数学科学学院,美国 [3]南昌大学土木建筑工程学院,江西南昌330013

出　　处：《应用数学》2020年第2期295-307,共13页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11461026,11661036)。

摘　　要：本文对一维常微分算子及发展微分算子提出一种基于解析多项式特解(MPPS)的求解方法,通过使用这些特解公式,将微分方程的解显式表达为多项式特解的线性组合来求解复杂的微分方程,如可以使用这些公式来求解右端具有不连续驱动项的微分系统.文中给出一系列数值例子,数值模拟结果精度很高,而且误差非常稳定.In the present paper,we present an analytical polynomial particular solutions method(MPPS)for solving various ordinary differential operators in the cases of timeindependent and time-dependent equations.By using these formulae,the solutions can be written explicitly in terms of monomial and we can obtain the approximate polynomial particular solutions for linear or nonlinear differential operators.For example,these formulae can be implemented to solve the differential system with discontinuous right hand side term.A series of numerical examples have been given with excellent results.These results show that our proposed method has high accuracy and corresponding errors are very stable for higher order polynomial basis functions.

关 键 词：多项式基函数 多项式特解法 常微分算子 

分 类 号：O241.8[理学—计算数学]