A Hp - Legerrdre - Gauss - Radau Spectrum Configuration Method For Arbitrary Continuous Delay Differential Equations

This paper mainly studies two different kinds of collocation methods for differential equations with piecewise continuous arguments, and analyzes their convergence respectively. The models of this kind of equations are widely used for many science ?elds, such as biology, electrodynamic and control science, etc. Therefore,researching this kind of equations is of important theoretical values and practical signi?cance.Firstly, the history of delay differential equations and differential equations with piecewise continuous arguments is introduced, and development status is reviewed. Secondly, some basic de?nitions of collocation methods are given and the Legendre-Gauss-Radau method is applied to solve differential equations with piecewise continuous arguments, and the corresponding convergence is analyzed. Finally,a new hp-Lengendre-Gauss-Radau is used to solve differential equations with piecewise continuous arguments, and the corresponding convergence is also investigated.By comparison, we know that the convergence condition of the hp-LegendreGauss-Radau method not only depends on the differential equations with piecewise continuous arguments, but also on stepsize. Therefore, we can always choose the stepsize to satisfy the convergence condition. However, the condition of convergence of the Legendre-Gauss-Radau method only depends on the differential equation itself. Hence, the hp-Legendre-Gauss-Radau method is better than the LegendreGauss-Radau method.