Abstract:
A method of collocation and interpolation of the power series approximate solution at some grid and off-grid points is considered to generate a continuous linear multistep method for the solution of general second order initial value problems at constant step size. We use continuous block method to generate independent solutions which serves as predictors at selected points within the interval ofintegration. The efficiency of the proposed method was tested and was found to compete favorably with the existing methods.

Abstract:
In this research work, we present the derivation and implementation of an order six block integrator for the solution of first-order ordinary differential equations using interpolation and collocation procedures. The approximate solution used in this work is a combination of power series and exponential function. We further investigate the properties of the block integrator and found it to be zero-stable, consistent and convergent. The block integrator is further tested on some real-life numerical problems and found to be computationally reliable.

Abstract:
A manually operated juice extractor was designed, constructed and evaluated 2005 at the Department of Agricultural Engineering, Federal college of Agriculture, Akure, Ondo State Nigeria. In Nigeria, fruit juices are obtained through hand pressing and electrically operated extractors. The hand pressing method is always tedious and time consuming. That of electrically operated is simple but the epileptic power supply is a limiting factor for its use. This manually operated juice extractor was designed and constructed to save time, improve efficiency, increase capacity and reduction in spoilage and waste. Performance evaluation was carried out with the production of orange and pineapple juices. The results showed that the machine produced efficiencies of 83.86 and 85.38% and extraction capacities recorded were 1.29 kg h 1 and 1.23 kg h 1 for orange and pineapple juices.

Abstract:
In this study, we investigate a note on the thermal ignition in a strongly exothermic reaction of a variable viscosity combustible material flowing through a channel with isothermal walls under Arrhenius kinetics, neglecting the construction of the material under physical and reasonable conditions to give further insight into the theory of combustion. Numerical solutions are constructed for the governing non linear boundary-value problem using shooting technique together with Runge-Kutta method and important properties of the temperature field and thermal critically are discuss.

Abstract:
The numerical solution of first order ordinary differential equations have been extensively discussed and well studied as reported in the literatures. Also the development of multistep schemes for solving second order ODEs there been presented by some members. In this presentation an attempt shall be made to develop a numerical scheme (multistep scheme) that can be used to solve third order and forth order ODEs directly without necessarily resolving this type of equations into system of first order ODEs.

Abstract:
Crude oil production industry as the hub of Nigeria Economy is not immune to the global financial meltdown being experienced world over which have resulted in a continual fall of oil price. This has necessitated the need to reduce cost of production. One of the major costs of production is corrosion cost, hence, its evaluation. This research work outlined the basic principles of corrosion prevention, monitoring and inspection and attempted to describe ways in which these measures may be adopted in the context of oil production. A wide range of facilities are used in crude oil production making it difficult to evaluate precisely the extent of corrosion and its cost implication. In this study, cost of corrosion per barrel was determined and the annualized value of corrosion cost was also determined using the principles of engineering economy and results analyzed using descriptive statistics. The results showed that among the corrosion prevention methods identified, the use of chemical treatment gave the highest cost contribution (81%) of the total cost of prevention while coating added 19%. Cleaning pigging and cathodic protection gave no cost. The contribution of corrosion maintenance methods are 60% for repairs and 40% for replacement. Also among the corrosion monitoring and inspection identified, NDT gave the highest cost contribution of 41% of the total cost, followed by coating survey (34%). Cathodic protection survey and crude analysis gives the lowest cost contribution of 19% and 6% respectively. Corrosion control cost per barrel was found to be 77 cent/barrel. The significance of this cost was not much due to high price of crude oil in the international market. But the effect of corrosion in crude oil processing takes its toll on crude oil production (i.e. deferment).

Abstract:
Direct numerical solutions of second and higher order ODEs have constituted a major problem in the resent past. In order to seek for numerical solution of equations of these types, one have to resolve the equations into a system of first order ordinary differential equations before solving the resulting equations with any desired known methods. In an attempt to do this, it often takes a very long period of time and the task is always laborious. In order to circumvent this problem, we were led to this present study. Here, we decide to come up with a multistep method which is more accurate and more efficient with very small error constant in solving second order ordinary differential equations without resolving into system of first order ordinary differential equations. The method used here is based on collocating and interpolating at k and k-1 points respectively where k = 6. This yields a 6 step method which is symmetric, zero stable and constituent. Some numerical examples were given to illustrate the desirability and efficiency of this method.

Abstract:
We studied the effect of radiation on a hydromagnetic flow of a radiating gas where the thermal conductivity depends linearly on the temperature of the system. The energy equation in an optically thin limit case was considered. The problem is reduced to a non-linear partial differential equation. Successive approximation method is employed to study the problem. It was observed that an increase in radiation parameter causes a decrease in temperature.

Abstract:
In this study, we shall present the derivation and application of some linear multistep methods in solving initial value problems for first order Ordinary Differential Equations (ODES) using canonical polynomials as basic functions. By interpolating and collocating at some selected points, some important classes of linear multistep methods were generated. The methods derived shall be compared with well known Adams Moulton method of the same order. Some numerical examples were given to illustrate the effectiveness of these methods.

Abstract:
A mathematical model and its associated numerical search algorithm has been
developed for routine coal blending to include local coals for cokemaking at the
Nigerian blast furnace-based Ajaokuta Steel Plant. A typical binary blend proposed
using the model includes 28.38% and 29.00% of the ash- laden Lafia and non-caking
Okaba coals, respectively. The proposed blends satisfy basic chemical and mechanical
strength requirements at the lowest cost per ton of coal. The blending calculations
showed that only low ash, low sulphur, medium volatile and high vitrinite reflectance
prime grade coals such as the UK Ogmore should be imported for blending with the
ash-laden medium coking Lafia coal. When the proposed blends are successfully
confirmed with bench and pilot scale carbonization tests, cokemaking at Ajaokuta will
be conducted with substantial savings in foreign exchange.