A Zero-Stable Numerical Model as First, Second, and Third-Order Initial Value Problems Solver

This paper addresses solutions of multi-order ordinary differential equations (ODEs) using a single formulated scheme. The use of a block method to solve initial value problem of a specific order has attracted a lot of attention in the literature. The discrete method is formulated from continuous schemes obtained via collocation and interpolation techniques and applied in a block-by-block manner as a numerical integrator for first, second and third-order ODEs. The convergence properties of the method are discussed via zero-stability and consistency, and on investigation, the proposed method is found to be convergent. Solutions of the test problems considered are presented, as well as comparisons to existing approaches in the literature.