Derivation of One-Sixth Hybrid Block Method for Solving General First Order Ordinary Differential Equations

Abstract

This paper focuses on the derivation of one-sixth hybrid block method for the general solution of first order initial values problems of ordinary differential equations. The new proposed method was derived by using the approach of collocation and interpolation of Chebyshev polynomials, approximate solution at some selected points to get a continuous linear multistep method, which was evaluated at some off-grid points to generate hybrid linear multistep methods. Basic properties of the proposed method wasexamined and the method found to be zero-stable, consistent and convergent. The efficiency of the method was tested on some numerical examples and in particular, on well-known SIR Model, Prothero-Robinson oscillatory problem and highly stiff oscillatory problem. On comparison, the new proposed method performed favourably when compare with the existing method proposed by other researchers in the area of Numerical Analysis.