FSAL explicit two-step hybrid method for solving special second-order initial value problems

Abstract

In this paper, a new FSAL explicit two-step hybrid method for solving second-order differential equation of the form y" = f (x, y) is proposed. The new method is constructed using the order conditions based on fifth-order of explicit two-step hybrid method developed by Franco (2006). The stability analysis is determined by the interval of periodicity and the interval of absolute stability. The numerical experiments are carried out using a wide range of problems to illustrate and support the efficiency of the suggested method. The numerical results show that the new method has smaller maximum error than the explicit two-step hybrid method of order five and order six.