The Formation of Implicit Second Order Backward Difference Adam’s Formulae for Solving Stiff Systems of First Order Initial Value Problems of Ordinary Differential Equations
Sabo J. *
Department of Mathematics, Adamawa State University, Mubi, Nigeria.
Kyagya T. Y.
Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.
Ayinde A. M.
Department of Mathematics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The formation of implicit second order backward difference Adam’s formulae for solving stiff systems of ODEs was study in this paper. We used interpolation and collocation in deriving backward differentiae Adam’s formulae. The basic properties of our method was analyzed, and it was found to be consistent, zero-stability and convergent, we further plotted the region of absolute stability and it was shown to be A-stable. Numerical evidences shows that the multistep method develop is very effective method for in handling linear ODEs either initial value problems or boundary value problems.
Keywords: Implicit second order, backward difference, Adam’s formulae and ODEs