NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS  

作　　者：Xiaoli DING Yaolin JIANG 丁小丽;蒋耀林(Department of Mathematics, Xi'an Polytechnic University;Department of Mathematics, Xi'an Jiaotong University)

机构地区：[1]Department of Mathematics,Xi＇an Polytechnic Universit [2]Department of Mathematics,Xi＇an Jiaotong Universit

出　　处：《Acta Mathematica Scientia》2018年第3期756-768,共13页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of China(NSFC)under grant 11501436;Young Talent fund of University Association for Science and Technology in Shaanxi,China(20170701)

摘　　要：Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.

关 键 词：Fractional differential-algebraic equations nonnegativity of solutions waveform relaxation monotone convergence 

分 类 号：O175[理学—数学]