Multiderivative Runge-Kutta Methods For Linear Discrete Delay Systems

Linear discrete delay differential equations are widely applied in many fields, such as electrical,optical and engineering control. The importance is self-evident. But the true solution of such equations is not easy to get. However, seeking the numerical solution of numerical methods, although not a true solution of the equation, but as long as the choice of appropriate methods, numerical solution is also very effective. This article will introduce Multiderivative Runge-Kutta methods which are proposed for a class of initial value problem of ordinary differential equation. So this article will apply multi-derivative Runge-Kutta method to linear discrete delay differential equations, which launched new research. In this article, multiderivative Runge-Kutta methods mainly launched following a series of studies.The first chapter gives the course of research and development of linear discrete delay differential systems studied in this paper, including the findings of stability, convergence and other properties. Then describes the development of multiderivative Runge-Kutta methods.The second chapter describes the issues discussed in this article and the extended multiderivative Runge-Kutta methods. In this part, the linear discrete delay problem is introduced, and the general form of the extended multiderivative Runge-Kutta method is given. On this basis, the introduction of linear operators, gives its multi-derivative Runge-Kutta methods containing the corresponding operator.The third chapter describes the convergence criterion of multiderivative Runge-Kutta method for solving linear discrete delay systems. Then this solution is verified by numerical experiments.The fourth chapter describes the boundedness criterion and asymptotic stability criteria of multiderivative Runge-Kutta method for solving linear discrete systems with delay. This section gives numerical experiments to verify the above conclusion...