On Some Properties of Multistep Second Derivative Methods with Constant Coefficients

Abstract

Construction and application of the Multistep Second derivative methods usually is connected with the name of Ştörmer, who was the first to construct such methods. This method in one version is fully investigated by Dahlquist. Since the beginning of 20 th century, new areas of mathematics have emerged, the research of which was formulated using Ordinary Differential Equations, ones with a special structure. New modifications have appeared in Multistep Second derivative Methods with constant coefficients. This method is called the Ştörmer or Methods with special structure. Recently have constructed similar methods using other ways, such as using the Spline function used in the power series. Here, for this purpose, the Multistep Second derivative method with constant coefficients is used. All the methods with Second derivative have compared, have given some recommendation for their application, to solving some initial-value problems. Constructed concrete methods some of them have applied to solve model problems. Note that, have defined the condition, which usually have imposed on the coefficients of the Multistep Second derivative methods.