Research Papers/Topics in Industrial Mathematics

Hamiltonian Approach for Constrained Optimization

The Hamiltonian approach for constrained optimization is indeed a useful tool in the hands of the economists, scientists and statisticians who applied it in the modelling of optimization problems. It can be noted that the treatise in this research work is an eye opener for a better understanding, application and utilization of the method as we exploit its vitality to solving optimization problems. Though, the approach seems to be a derived approach from existed ones but also intens...

Numerical Solution of a One-Dimensional Second Order Macroscopic Traffic Flow Model with a Source Term.

The study of traffic models has given rise to many models with the aim of realistically determining the behavior of traffic. The dynamics of the macroscopic traffic flow is modeled by a partial differential equation, where the object of study is to determine the density of traffic flow. We derived a second order macroscopic traffic flow model equation from a first order one using the Fick’s law of diffusion. We formulated second order macroscopic traffic flow model equation with a sourc...

Adam-Bashforth Iterative Scheme for Initial Value Problems

ABSTRACTIn this project work, we studied the Adams-Bashforth scheme for solving initial value problems. We gave an indebt explanation on the Adam-Bashforth scheme, its consistency, stability, and convergence, the two and three step methods were also derived. Numerical solutions were obtained using four (4) examples.TABLE OF CONTENTS Cover page                        i                                                                            ...

MULTI-DERIVATIVE HYBRID METHODS FOR INTEGRATION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATION WITH INITIAL CONDITIONS

ABSTRACTIn this study, new multi-derivative hybrid methods for the integration of general second order initial value problems ofordinary differential equations are considered. Linear multistep formula was used in the development of the methodstaking Taylor series as the basis function. For the methods K=1 and K=2, the unknown parameters was solved forusing systematic reduction of simultaneous nonlinear equations. Due to the lapses in number of equations compared tothe number of unknowns, we m...

Application of Shooting Method and Finite Difference Method in Providing Solution to Two Boundaries Value Problems

This paper investigates the efficacy of the shooting method and finite difference method in the numerical solution of two point boundary value non linear problems. The difficulty in providing exact solutions to two point boundary value problems via analytical methods necessitated the study. The shooting method which utilizes the Runge-Kutta method as integrator provides us with a better approximation to the solution than the finite difference method which utilizes second order, central differ...

Application of Forward Difference Operator on Sequence of numbers

A new formula based on forward difference operator is derived herein, the formula is used to compute the nth term and sum (Sn) of an Arithmetic progression. The merit of using the formula is that if given ,  the nth term of an A.P can be easily and quickly computed if n is not known.