On One Justification on the Use of Hybrids for the Solution of First Order Initial Value Problems of Ordinary Differential Equations

Abstract

This paper is aimed at discussing and comparing the performance of standard method with its hybrid method of the same step number for the solution of first order initial value problems of ordinary differential equations. The continuous formulation for both methods was obtained via interpolation and collocation with the application of the shifted Legendre polynomials as approximate solution which was evaluated at some selected grid points to generate the discrete block methods. The order, consistency, zero stability, convergent and stability regions for both methods were investigated. The methods were then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The results revealed that the hybrid method converges faster than the standard method and has minimum absolute error values.