二次Riccati方程研究综述  

Review of Quadratic Riccati Equation

作　　者：刘玉堂[1] 辛祥鹏[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2017年第3期21-27,共7页Journal of Liaocheng University:Natural Science Edition

基　　金：国家青年科学基金项目(11505090);山东省自然科学基金中青年科学家奖励基金(BS2015SF009)资助

摘　　要：本文首先介绍了Riccati方程的基本情况,包括研究的部分成果和重要意义.然后按国内和国际两类文献陈述了从2014年至今Riccaiti方程的研究进展.对这两类文献又从方程本身的性质、可积性、精确解、数值解、定性理论和Riccati方程的应用等角度分别介绍了国内外的研究情况.从中可以看出,求解仍是学者们研究Riccati方程工作的重点,对它的应用主要是寻求其他微分方程的精确解,实际应用方面的工作较少.A brief basic situation of the Riccati equation is introduced including some results and the significance of its research.The research progress of the Riccait equation is analyzed from domestic and international literatures from 2014 to the present.The research situation are expounded at home and abroad in the view of the nature of the equation itself,integrable properties,exact solutions,numerical solutions,the qualitative theory and the applications.It can be seen that the solutions is still the focus of the study of the quadratic Riccati equation,and its application is mainly to find exact solutions to the other differential equations,the practical application of the quadratic Riccati equation is rarely done.

关 键 词：二次Riccati方程 精确解 解的性质 Riccati方程的应用 

分 类 号：O175.2[理学—数学]