Numerical Methods For Solving Two Classes Of Nonlinear Impulsive Differential Equations

Impulsive differential equations（IDEs）are widely used in biology,infec-tious diseases,economics,physics and control systems.In general,the analytical solutions of IDEs are difficult to solve,so it is significant to study their numer-ical methods.Most of the researches on the numerical methods for nonlinear impulsive differential equations are based on the one-sided Lipschitz condition in the inner product space.If the one-sided Lipschitz constant of the problem is very large,the conclusions of the above stability analysis will be distorted.Therefore,it is necessary to study the stability of numerical methods in more general Banach spaces.On the other hand,there are few studies on the high-order numerical methods for nonlinear impulsive delay differential equations,so it is necessary to study the numerical methods of higher-order convergence.In view of the above discussion,this paper gives the following study results（1）The multistage one-step multiderivative methods for solving the prob-lem classK^p（μ,λ,ζ）of nonlinear impulsive differential equations is given in Banach space,and asymptotic stability results for this methods are obtained;（2）A higher-order numerical scheme is constructed based on the modified block-by-block method for nonlinear impulsive delay differential equations,and we prove that the method is convergent of the order 4.Finally,numerical experiments are given to verify the correctness of the conclusions.