Research And Structure On Linear Multistep Method Formulas Of Initial Value Problems In Ordinary Differential Equations

In this paper, the linear multistep formulas of the initial-value problem in ordinary differential equations are further researched on the base of the present situation. On the base of definition of the basic formulas, all linear 4 step method basic formulas are deduced and convergent formulas form them are chose out. The orders, error and stability of them are researched and further studied. And a new method of structure linear multistep formulas is given.The major tasks in this paper include:Firstly, all linear 4 step method basic formulas are deduced on the base of defining the basic formulas.Furthermore, by means of the convergent condition of the linear multistep method, all convergent formulas of 4 step basic formulas are received using symbol operation of Matlab. And formulas coefficients, errors coefficients, orders and intervals of absolute stability are researched.Finally, a new method of structure linear multistep formulas is given. At the same time, the theory and the criteria of judging received new formulas are given. In this paper, two numerical experiments are given and formulas coefficients, errors coefficients, orders and intervals of absolute stability are studied. Some excellent formulas are received. They are proved to be more effective than two original formulas for solving stiff ordinary differential equations.In this paper, much work is done for both theoretical research and application of the numerical method in the initial-value problem and the stiff problem in ordinary differential equations.