About Some Applications Multistep Methods with Constant Coefficients to Investigation of Some Biological Problems |Biomedgrid

In our life we very often meet with mathematical models for which are described by using Ordinary Differential Equations. These equations are studied starting from the epoch of Newton. Therefore, many scientists believe that it is impossible to find something new in this area. However, it is not. We will show that in this area one can construct numerical methods for solving these equations, which have some advantages. Here it has been shown that it is possible to construct a stable method having a higher order of accuracy than the known. For this here is suggested to use the multistep methods having the advanced and hybrid types. To consider the construction of methods with new properties on the intersection of the above mentioned. methods. As is known, models for much biological research are described by the ordinary Differential equation, and the methods studied here can be applied to solving above mentioned problems. Therefore, here found the maximum value for the order of accuracy of the stable methods having the advanced and hybrid types. And considered to define the maximum value for the stable methods constructed on the intersection of these methods. By the application some of specific methods to solve model problems, have demonstrated the advantages of the proposed methods. By considering that in the investigation of multistep methods one of the basic questions is the determine the necessary condition of its convergence, here have defined the conditions, which are imposed on the coefficients investigated methods. For obtaining reliable information on the solution of the problem under study suggested to use the bilateral methods. For the illustration of this have constructed simple bilateral stable methods, which have applied to solve model problems. And, given a sequence studying the conception of stability for multistep methods in terms of history. The receiving results here are illustrated on solving some model problems, with the methods suggested here.