Some stiffly stable second derivative continuous linear multistep methods with a hybrid point for stiff IVPS in ODEs

Based on Gear¡¦s fixed step size backward differentiation methods, Gear (1968), second derivative continuous linear multistep methods with an off-step point are presented. This type of methods provides a means of bypassing the order barriers imposed by Dahlquist (1963) and also provides continuous solutions of IVPs in ODEs. The stiff stability of these methods is determined by using the boundary locus. Instability sets in at k ƒ­10 . Numerical results of the methods solving a non-linear and a linear stiff initial value problems in ordinary differential equations are compared to that of the state -of -the-art code, ODE 15s in MATLAB

Crude Oil-Degradation and Plasmid Profile of Nitrifying Bacteria Isolated from Oil-Impacted Mangrove Sediment in the Niger Delta of Nigeria

The crude oil degradability and plasmid profile of autotrophic nitrifying bacteria, Nitrosomonas and Nitrobacter species, isolated from mangrove sediment in the Niger Delta of Nigeria were studied. The effects of temperature, pH and optical density on the utilization of different carbon sources by the bacteria were also investigated. Results showed that nitrifying bacteria could utilize kerosene, diesel oil, jet fuel and engine oil as carbon sources. None utilized hexane and xylene but moderate growth was observed in benzene, phenol and toluene. However, their ability to utilized crude oil varied both in rates of utilization and in growth profiles. Mixed culture of the isolates degrades 52 % of crude oil introduced into the medium followed by Nitrosomonas sp. with 40 % degradation. The least was Nitrobacter sp. with 20 % degradation. The ability of the autotrophs to degrade crude oil was found to be plasmid-mediated through curing experiment and electrophoresis. The size of the plasmid involved was estimated to be 23 kb. The high crude oil utilization of the mixed culture implies that nitrifying bacteria isolated from contaminated ecosystem are excellent crude oil degraders and can be harnessed for bioremediation purposes

Polycyclic Aromatic Hydrocarbon-degrading Bacteria from Aviation Fuel Spill Site at Ibeno, Nigeria

Polycyclic aromatic hydrocarbon (PAH)–degrading bacteria were isolated from aviation fuel contaminated soil at Inua Eyet Ikot in Ibeno, Nigeria. PAH-degrading bacteria in the contaminated soil were isolated by enrichment culture technique. Isolates with high PAH degrading potential characterized by their extensive growth on PAH-supplemented minimal salt medium were screened for their naphthalene, phenanthrene and chrysene degradability. The screening medium which contained selected PAHs as the sole source of carbon and energy showed that Micrococcus varians AFS-2, Pseudomonas putida AFS-3 and Alcaligenes faecalis AFS-5 exhibited a concentration–dependent growth in all the PAH–compounds tested. There were visible changes in the color of growth medium suggesting the production of different metabolites. Their acclimation to different PAH substrates was also evident as A. faecalis AFS-5 isolated from chrysene grew well on other less complex aromatic compounds. The isolate exhibited best growth (0.44 OD600) when exposed to 10 ppm of chrysene for 5 days and could utilize up to 90 ppm of chrysene. This isolate and others with strong PAH-degrading potentials are recommended for bioremediation of PAHs in aviation fuel-contaminated sites in the tropics

A Special Family of LMM with Two Hybrid Points for Stiff ODEs

Hybrid methods with one or more off-step points give better stabilitycharacteristics and higher order than the conventional linear multistep methods (LMM). Enright (1974) discussed the formulation of the second derivative LMM which was found to be stiffly stable for step number k £ 7 for the numerical solution of stiff Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). In this paper some second derivative  continuous linear multistep methods with two hybrid points are proposed for step number k £ 9 for stiff ODEs. The derivation of these methods is based on collocation and interpolation approach of Onumanyi et al (1996)and Arevalo et al (2002). The family of methods is stiffly stable for k £ 8 and of comparable accuracy to the Enright’s method and the state of-the-art code Ode 15s in MATLAB.Keywords: , Hybrid points, Continuous LMM, stiffly stable

The Numerical Integration of Stiff Systems of ODEs using Stiffly Stable Continuous Second Derivative Hybrid Methods

A class of continuous second derivative hybrid methods is developed and the stability of these methods is investigated using the root locus plot. The k-step stiffly stable schemes of order k + 2 are suitable for stiff systems of equations for k ≤ 14 . These schemes have been implemented and some numerical results are presented.Keywords: Continuous Linear Multistep Methods, Hybrid Predictor, Stiff Stability, Root Locus

Indigenous Knowledge In Imo State: A Case Study Of Ife Community In Ezinihitte Local Government Of Imo State, Nigeria

The study examined the availability, types, utilization, dissemination and documentation of indigenous knowledge in Ife Community of Ezinihitte Mbaise Local Government Area of Imo State, Nigeria. Structured interview schedule was used for data collection. Ten respondents were interviewed from each village in Ife making a total of eighty respondents. The result of the study showed that the people of Ife Community still practice and utilize different types of indigenous knowledge in the area of agriculture, health, food preparation, Local craft and industry, history/culture. Result also revealed that dissemination of indigenous knowledge is still from parents to children, learning through observation, learning through participation and from master to apprentice. It was also discovered that there have been no serious effort to document this knowledge either by inhabitance of Ife Community in Ezinihitte Local Government and Imo State Government.Based on the finding of this research recommendation were made with a view to disseminate, document and preserve indigenous knowledge using the new information and communication technology so that this knowledge will not be lost forever

Variable order one-step methods for initial value problems I

A class of variable order one-step integrators is proposed for Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). It is based on a rational interpolant. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 91-9