Convergence Analysis Of Hp-Legendre-Gauss Collocation Method For A Class Of Impulsive Delay Differential Equations

Impulsive delay differential equations are widely used in many fields of science and engineering.The research of their numerical methods is of unquestionable importance.In this paper,the convergence of hp-Legendre-Gauss collocation method is studied for a class of impulsive delay differential equations.Firstly,the Legendre-Gauss collocation method is used to solve a class of impulsive delay differential equations,the error analysis shows that the method is convergent and has spectral accuracy.However,the convergence condition is closely related to the equation itself,so it cannot be improved and has great limitations.Therefore,the hp-Legendre-Gauss collocation method for solving the problem is obtained by improving the method,the error analysis shows that the method is convergent and has spectral accuracy,the convergence condition is not only related to the equation itself,but also related to the step size.We can always find the appropriate step size to satisfy the convergence condition.The validity of the proposed theory is also verified by the related numerical experiments.