

Articles
by
H.K. Oduwole 
Total Records (
2 ) for
H.K. Oduwole 





J.O. Fatokun
and
H.K. Oduwole


This study concerns the derivation of higher order Newtoncotes closed integration using Lagrange’s interpolation polynomial functions. In literature, the conventional way of deriving these integration formulae is by making the x_{i }equally spaced, so that there are only n+1 parameters a_{i} to choose. The coefficients are then fixed either by using finite difference results or by considering it as a general formula with various coefficients which must be fixed. William presents coefficients for orders p = 1, 2,...8 . In this research, an extension of this was carried out for orders p = 9, 10, 11. Ralston gave a detailed mathematical treatment of the error analysis for the known Newton Cotes formulae of orders p=1,2,…,8. These manipulations are extremely cumbersome since it involves n+1 conditions and hence solving a large system of algebraic equations. This led to the new approach of using the Lagrange’s interpolation functions to derive the Newton Cotes Closed formulae of orders p = 1,2,…,11. A generalized formula was developed for order p=k. These methods were applied to some integrals such as exponential function and trigonometric functions. The numerical results show that higher order methods are needed for equally spaced intervals to increase the accuracy of the general Newtoncotes closed formulae. 





A.R. Kimbir
and
H.K. Oduwole


A mathematical model of HIV/AIDS transmission dynamics is proposed considering counselling and Antiretroviral Therapy (ART) as major means of control of infection. Threshold conditions are derived, in terms of the given model parameters, for the existence and stability of the diseasefree and endemic equilibrium states of the model, as well as the proportion of infected people to receive ART. Analytical and numerical results obtained indicate that ART and counselling could be effective methods in the control and eradication of HIV/AIDS. 





