New Efficient Numerical Model for Solving Second, Third and Fourth Order Ordinary Differential Equations Directly

Abstract

This article presents a two-step hybrid linear multistep block method for solving second, thirdand fourth order initial value problems of ordinary differential equations directly. The derivationof the method was done using collocation and interpolation techniques, while approximatedpower series was used as an interpolating polynomial. The fourth derivative of the power serieswas collocated at the entire grid and off-grid points, while the fifth and sixth derivatives of thepolynomial were collocated at the endpoint only. The basic properties of the developed method,that is, order, error constant, zero stability, region of absolute stability, convergence andconsistency of the method were properly investigated. The numerical results demonstrated thatthe scheme developed handles: second, third and fourth order ordinary differential equationsefficiently and accurately when compared with existing methods. The proposed method takesaway the burden of developing a separate method for the solution of second, third and fourthorder initial value problem of ordinary differential equations.