On the Comparison of Adam-Bashforth and Adam Moulton Methods for Non-Stiff Differential Equations
Osakwe Charles Nnamdi
Department of Mathematics, Faculty of Natural and Applied Science, Nasarawa State University, Keffi, Nigeria.
Olobayo Solomon Adelaja
Department of Mathematics, Faculty of Science, University of Jos, Jos, Nigeria.
Omowo Babajide Johnson *
Department of Mathematics, Faculty of Natural and Applied Science, Nasarawa State University, Keffi, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents the comparison of the two Adams methods using extrapolation for the best method suitable for the approximation of the solutions. The two methods (Adams Moulton and Adams Bashforth) of step k = 3 to k = 4 are considered and their equations derived. The extrapolation points, order, error constant, stability regions were also derived for the steps. More importantly, the consistency and zero stability are also investigated and finally, the derived equations are used to solve some non-stiff differential equations for best in efficiency and accuracy.
Keywords: Adam-Bashforth, Adam Moulton, accuracy, stability region, consistency, zero stability