Diagonal Implicit ERKN Method For Symmetry Of Oscillatory Reversible Differential Equations

In the field of hydrodynamics,now optics,aerospace,chemical and chemical and other high-tech fields.Most of the phenomena that evolve over time can be described by various complex differential equations,so the study of the numerical solution of the reversible differential equation is very important.In the past study,we mainly use the Runge–Kutta–Nystr¨om(RKN)method to research the numerical solution of the inverse differential equation,and then the explicit symmetric extended Runge–Kutta–Nystr¨om(ERKN)method is adopted.However,the implicit symmetric ERKN method has not been studied in depth.This research contains five parts.The first part is mainly about the research background and research significance of the oscillation reversible differential equation.The second part tells about the definition and theorem of the order condition and symmetric condition.This paper is mainly to construct the symmetric diagonal implicit ERKN method.Therefore,in this paper,the most important content is the third part,using the symmetric condition and the order condition to construct six kinds of simple diagonal implicit method.In the fourth part,we discuss the stability of the construction method.In the last part,we do numerical experiment on three group of random numerical solution and obtain the effect picture.By the effect picture,we construct the method in the oscillation reversible system advantage is very obvious.