Additive parameters methods for the numerical integration of y″ = f (t, y, y′)

Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh

“…Chawla [6] analysed a super-stable two-step scheme for the numerical solution of general second-order IVPs. In order to stabilize the method, Rai and Ananthakrishnaiah [ [7] , [8] ] used the additive parameters technique for the numerical solution of second-order IVP. Coleman [9] proposed order conditions for a family of two-step methods for the solution of second-order nonlinear IVP without first-order derivative terms.…”

Variable Order Block Method for Solving Second Order Ordinary Differential Equations

“…There are various direct solvers discussed in the literature. For instance, Runge-Kutta method (Ismail et al 2016), Runge-Kutta-Nyström method (Chawla & Sharma 1985), hybrid method (Jator 2010;Kambo et al 1983), additive parameters method (Sesappa Rai & Ananthakrishnaiah 1996), and block method (Chien et al 2018;Ismail et al 2018;Waeleh & Majid 2017;Zainuddin et al 2014), to name a few. Block method were first introduced by Milne (1953) as a means of obtaining starting values for predictor-corrector schemes.…”