Development of Third Derivatives Falkner-Type for the Solution of Second Order Differential Equations - Akanji, Semiyu; Mohammed, Umaru; Abdullahi, Habibah (FUDMA Journal of Sciences, 2026)
Second-order ordinary differential equations frequently arise in scientific and engineering applications and efficient numerical methods are often required when analytical solutions are difficult or impossible to obtain. In this paper, a Falkner type method for k = 2 with two off-step point were derived for the 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 analysed and the methods were found to be consistent, zero stable and hence convergent. Numerical experiments were carried out on three (3) problems of second order initial value problem (IVP). The results obtained for the proposed methods in comparison with the exact solutions and some existing methods from the literature show the efficiency and reliability of the proposed schemes.