One-Step Five Offgrid Implicit Hybrid Block Method for the Direct Solution of Stiff Second-Order Ordinary Differential Equations

Abstract

A one-step five off-grid implicit hybrid block method for the solution of stiff Second Order Ordinary Differential Equations is developed. The continuous hybrid linear multistep method was generated using power series approximation via interpolation and collocation at the grid points. The discrete block method was recovered by evaluating the continuous block method at some selected grid points. The method is convergent. Numerical experiments on some Second Order Ordinary differential equations show that the method is more accurate than some existing methods.