Development of Falkner-Type method for Numerical Solution of Second Order Initial Value Problems (IVPs) in ODEs

Abstract

In this research work, Falkner type method for k=2 with four off-step point were derived for numerical solution of second order initial value problems. The idea of collocation and interpolation techniques was adopted in the derivation of the schemes. The basic properties of numerical methods were analyzed and the methods were found to be consistent, zero stable and therefore, convergent. Numerical experiments were carried out on five (5) problems of second order initial value problems (IVPs). The results obtained for the proposed methods, in comparison with the exact solutions and some existing methods from the literatures show the efficiency and reliability of the proposed schemes