An Analysis Of The Structural And Stability For Linear Multi Step Methods

The movement of a large number of practical problems,only in the mathematics model was established by partial differential equation. However, when we encountered some slightly more complex movement in a number of practical problems,differential equations can only be used to build its model. Among these established differential equations,only a handful of its theoretical solution can be solved. Therefore, numerical solutions of differential equations become very essential.This paper discusses several constructed forms of linear multi-step methods of ordinary differential equations.Firstly, we briefly introduce the research background of this article, research status and some basic concepts the numerical methods of differential equations.The second part of the article,we give three definitions and specific solution process of explicit Adams methods:numerical integral methods the first undetermined coefficient method and the second undetermined coefficient method. Similarly, three definitions and specific solution process of Backward differentiation formula (Gear mthods) are given.The third part of the article, according to the equivalence theorem of order, we got a linear and two step method with a parameter through calculation. Besides, the A-stability conditions of such methods are obtained by using the boundary locus method.Finally,the midpoint formula is applied to solve a class of two order delay differential equations, the characteristic equations are obtained for the model equation,by using the boundary locus method, the numerical solution and the theoretical solution of the compatibility of the results was obtained.