The Necessary Conditions Imposed on the Coefficients of Multistep Hybrid Methods Adapted for Solving ODEs of the Second Order

Abstract

There are some classes of methods to solve the initial-value problem for the ODEs of the second order. Recently among of them are developed the numerical methods, which are using in the application of computer technology. By taking into account the wide application of the numerical methods, here has investigated the numerical solution of the above-mentioned problem. For this aim here has constructed the multistep hybrid method with the special structure, which has been applied to solve the initial-value problem of the ODEs of the second order. Given some recommendation to choosing of the suitable methods for solving above named problem and also, have found some bounders imposed on the coefficients of the convergence methods. Constructed specific methods solve the initial-value problem for ODEs of the second order. The received theoretical results have been illustrated by using some concrete methods, which have applied to solve model problem for ODEs of the second order