Analysis of Accuracy, Stability, Consistency and Convergence of an Explicit Iterative Algorithm

Abstract

In this work, an analysis is carried out vis-à-vis an explicit iterative algorithm proposed by Qureshi et al (2013) for initial value problems in ordinary differential equations. The algorithm was constructed using the well – known Forward Euler’s method and its variants. Discussion carries with it an investigation for stability, consistency and convergence of the proposed algorithm-properties essential for an iterative algorithm to be of any use. The proposed algorithm is found to be second order accurate, consistent, stable and convergent. The regions and intervals of absolute stability for Forward Euler method and its variants have also been compared with that of the proposed algorithm. Numerical implementations have been carried out using MATLAB version 8.1 (R2013a) in double precision arithmetic. Further, the computation of approximate solutions, absolute and maximum global errors provided in accompanying figures and tables reveal equivalency of the algorithm to other second order algorithms taken from the literature.

Keywords: Iterative Algorithm, Ordinary Differential Equations, Accuracy, Consistency, Convergence.