ABOUT ONE INNOVATION NUMERICAL METHOD FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDERS

Objective: This study aims to explore the development of the Multistep Multiderivative Methods with constant coefficients and application that to solve.   Theoretical Framework: The numerical solution of initial value problem for the ODEs of high order was taken as the solution of the initial-value problem for the ODEs of the first order, which has been illustrated by using a simple model problem. Here have, constructed the innovative method, which applies to solve some model problems for the illustration advantages of such methods. Here, basically made the connection between degree and order for the stable Multistep Multiderivative methods, which is usually called as the law for degree of the Multistep Methods with the constant coefficients.   Method: This study used the multistep Multiderivative Methods with the constant coefficients   Results and Discussion: Have investigated the Multistep Thirdderivativese Methods including Multistep second derivative methods. These methods have comparised in fully form and find a law to dermined the maximum accuracy for stable Multistep Multiderivative Methods.