Four and Five-Point Integrators for the Solution of Systems of Stiff Initial Value Problems

Samuel Adamu; Musa Kida; Kefas Bitrus

doi:10.4314/cajost.v2i2.44

Authors

Samuel Adamu Basic Sciences Department, Federal College of Freshwater Fisheries Technology, New Bussa, Niger, Nigeria
Musa Kida Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria
Kefas Bitrus Department of Mathematical Sciences, Federal University Lokoja, Kogi State, Nigeria

DOI:

https://doi.org/10.4314/cajost.v2i2.44

Keywords:

Second derivative, 4-point block integrator, 5-point block integrator, Stiff initial value problems

Abstract

Four and five-point second derivative hybrid block integrators were developed
for the solution of stiff Ordinary Differential Equations (ODEs) using polynomial
approximate solution. Collocation and interpolation technique was adopted in
the development of the methods where collocation points were determined
using standard collocation method. The stability properties of the new
integrators were established and the efficiency of the integrators were tested on
some numerical examples with a written program using MATLAB 8.5, where
g − values were computed in addition to computation of f − values at
the internal stages. The results show that, the new integrators are efficient for
the solution of stiff Initial Value Problems (IVPs) of first order ODEs.