School of Physical Sciences (SPS)
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School of Physical Sciences (SPS)
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Item REFORMULATION OF TWO STEP IMPLICIT LINEAR MULTI-STEP BLOCK HYBRID METHOD INTO RUNGE KUTTA TYPE METHOD FOR THE SOLUTION OF SECOND ORDER INITIAL VALUE PROBLEM (IVP)(2025) ALIYU Abubakar; MUHAMMAD Raihanatu; ABDULHAKEEM YusufSecond-order ordinary differential equations (ODEs) is unavoidable in scientific and engineering fields. This research focuses on the reformulation of two-step implicit linear multistep block hybrid method into a seven-stage Runge-Kutta type method for the solution of second-order initial value problems (IVPs). A two-step, four-off-grid-point implicit block hybrid collocation method for first-order initial value problems was derived. Its order and error constants were determined, which shows that the schemes were of order 8, 8, 8, 8, 8 and 9 with respective error constants of , , , , . The derived block method was reformulated into a seven-stage Runge-Kutta type method (RKTM) for the solution of first-order ordinary differential equations; this reformulation was extended to handle the required second-order ordinary differential equations. The second-order Runge- Kutta-type method derived was implemented on numerical experiments. The method was found to be better than existing methods in the literature.Item METHOD INTO RUNGE KUTTA TYPE METHOD FOR FIRST ORDER INITIAL VALUE PROBLEM (IVP)(2025-03) Abubakar Aliyu; Raihanatu Muhammad; Abdulhakeem YusufProblems arises from science and technology are expressed in differential equations. These differential equation are sometimes in ordinary differential equations. Reliability with high accuracy and stability are necessary for a numerical method for the solution of differential equations. This research paper presents the analysis of a reformulated block hybrid linear multistep method into Runge-Kutta type method (RKTM) for first order initial value problems (IVPs). In view of this, the block hybrid method derived is of uniform order 6 with error constants of , , , and while the Runge-Kutta type method reformulated maintain the order of the derived block hybrid linear multistep method which are of uniform order 6 but with error constants of . Testing for convergence of both the derived block hybrid linear multistep method and the Runge-Kutta type method shows that the two methods are consistent and are also zero stableItem Production of biodiesel from Balanite aegyptiaca seed oil using chemical-activated catalyst produced from coconut shell(Nigerian Research Journal of Chemical Sciences, 2024) Alheri, A.; Ago, M. A; Jamila, U. A.; Anyanwu, S. K.,; Bisiriyu, M. T.; Aisha, K. UHeterogeneous catalyst produced from coconut waste shell (CWS) via chemical activation was utilized for biodiesel production from Balanite aegyptiaca seed oil. The effects of impregnation ratios (2 – 10 g/cm3), activation temperatures (500 – 900 oC) and time (1 – 3 h) on the yield of catalyst were investigated. The chemical-activated catalyst produced from coconut shell was characterized by Scanning Electron Microscopy (SEM) and Fourier Transform Infra-Red (FT-IR) spectroscopy. The biodiesel was further characterized using GC-MS. The heterogeneous catalyst produced by chemical activation under the following optimum conditions: activation temperature (800 oC), impregnation ratio (3:6g/cm3), and reaction time (1 h) was of high yield. SEM images showed a highly porous characteristic, with lots of cavities and strands on the surface. The optimum conditions to achieve maximum yield of the biodiesel (82.9%) were reaction temperature (40 oC), methanol/oil molar ratios (9:1 cm3), catalyst concentration (1.0 g/cm3) and reaction time (60 min). The fuel properties of biodiesel produced by chemical activation catalyst were: kinematic viscosity (5.70 mm2/s), specific gravity (0.86), pour point (9 oC), flash point (185 oC), cloud point (9 oC), colour 1.0 and cetane number 62. The GC-MS analysis demonstrated the presence of decanoic acid methyl ester, hexadecanoic acid, methyl ester, 4-hexenoic acid methyl ester and pentadecanoic acid methyl ester. The study showed that chemically produced heterogeneous catalyst from coconut waste shell can be used for the production of biodiesel.Item Assessment of Foliose Epiphytic Lichen (Parmelia sulcata) as Bioindicators of Atmospheric Trace Metals Pollution in Lapai Metropolis, Niger State(Science View Journal, 2024-01) Ibrahim, M.; Tsafe, A. I.; Gungshik, J. R.; Abdulkarim, A. M.; Zhikpe, Y. B.; Bisiriyu, M. T.The levels of atmospheric trace metals were determined using foliose epiphytic lichens (Parmelia sulcata) samples collected in eight (8) different locations within the residential areas and two control locations outside the residential area of Lapai town in Lapai local government of Niger State. A stratified random sampling technique was adopted and the analysis of the samples with atomic absorption spectrophotometer (AAS) gives the concentration (mg/kg) range of the metals as follows; 1.123-7.837 for Fe, 4.579-6.62 for Pb, 0.210-2.152 for Cr, 0.491-1.171 g for Ni, 0.018-0.983 for Cd, 0.057-1.471 g Zn, 0.198-1.287 for Mn, and 0.098-2.583 for Cu but Selenium was not detected in all the samples. The levels of some of these metals were slightly higher than the recommended USEPA (1993) limits but lower than FEPA (1991) limits. However, the distribution of these metals was not uniform across the samples, though their level was still at the background and very low compared to the reports on similar studies from industrialized areas of South-south and South-west Nigeria and other European countries. The variation in concentration of these metals at p≤0.05 indicates their source is mainly anthropogenic in origin. Epiphytic lichens validate the cost-effectiveness of this method for evaluating, assessing, and identifying depositional sources of the metals in the environment. The study revealed the atmospheric trace metal concentration of the area under study to be at a threshold level and hence the environment is still very safe from atmospheric trace metal pollution.Item An Appraisal on the Application of Reproduction Number for the Stability Analysis of Disease - Free Equilibrium State for S-I-R Type Models(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD) 2024, 2024-02-28) Abdurrahman, Nurat Olamide; Somma S. A.; Akinwande, N. I.; Ashezua, T. T.; Gweryina, R.One of the key ideas in mathematical biology is the basic reproduction number, which can be utilized to comprehend how a disease epidemic profile might evolve in the future. The basic reproduction number, represented by R0 , is the anticipated number of secondary cases that a typical infectious individual would cause in a population that is fully susceptible. This threshold parameter is highly valuable in characterizing mathematical problems related to infectious diseases. If R0 < 1, this suggests that, on average, during the infectious period, an infected individual produces less than one new infected individual, suggesting that the infection may eventually be eradicated from the population. On the other hand, if R0 < 1, every infected person develops an average of multiple new infections, it suggests that the disease may continue to spread throughout the population. We discuss the Reproduction number in this work and provide some examples, both for straightforward and complicated situations.Item Mathematical Modeling of Chemotherapy Effects on Brain Tumour Growth(International Conference and Advanced Workshop on Modelling and Simulation of Complex Systems, 2024-05-27) Abdurrahman, Nurat Olamide; Ibrahim, Mohammed Olanrewaju; Ibrahim, Jamiu OmotolaA brain tumor is an abnormal growth or mass of cells in or around the brain. It is also called a central nervous system tumor. Brain tumors can be malignant (cancerous) or benign (non-cancerous). In this work, we proposed a system of nonlinear differential equations that model brain tumor under treatment by chemotherapy, which considers interactions among the glial cells X(t), the cancer cells Y(t), the neurons Z(t), and the chemotherapeutic agent C(t). The chemotherapeutic agent serves as a predator acting on all the cells. We studied the stability analysis of the steady states for both cases of no treatment and continuous treatment using the Jacobian Matrix. We concluded the study with a numerical simulation of the model and discussed the results obtained.Item REDUCTION OF TOTAL ORGANIC CARBON AND BIOCHEMICAL OXYGEN DEMAND USING MODIFIED AND UNMODIFIED Hibiscus sabdiriffa AND Hibiscus esculentus STALKS: KINETIC AND ISOTHERM STUDY(Lapai Journal of Science and Technology, 2024) Anyanwu, S.K.; Sulaiman, M. I.; Tijani, J. O.; Suleiman, M.A.T.Item Population dynamics of a mathematical model for Campylobacteriosis(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD), 2024-02-22) Ashezua, T. T.; Salemkaan, M. T.; Somma, Samuel AbuThe bacterium campylobacter is the cause of campylobacteriosis, a major cause of foodborne illness that goes by the most common name for diarrheal illnesses. This paper develops and analyzes a new mathematical model for campylobacteriosis. It is demonstrated that in cases where the corresponding reproduction number is smaller than unity, the model's disease-free equilibrium is both locally and globally stable. The numerical simulation results indicate that increasing the treatment rate for both symptomatic and asymptomatic disease-infected individuals resulted in a decrease in the number of asymptomatic and symptomatic individuals, respectively, and a rise in the population's number of recovered individuals.Item Homotopy Perturbation Analysis of the Spread and Control of Lassa Fever(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD), 2024-02-22) Tsado, D.; Oguntolu, F. A.; Somma, Samuel AbuLassa fever, a viral infection transmitted by rodents, has emerged as a significant global health concern in recent times. It continues to garner significant attention daily basis owing to its rapid transmission and deadly nature. In this study, the Homotopy Perturbation Analysis was conducted to examine the spread and control of Lassa fever. The human population was categorized into susceptible, exposed, infected, and recovered compartments, while the rodent population was divided into susceptible and infected recovered compartments. By applying the Homotopy Perturbation Analysis to the nonlinear differential equations associated with these compartments, we were able to obtain the analytical solution for the spread and control of Lassa fever. The nonlinear differential equations were integrated into the Homotopy Perturbation framework and solved to form a power series solution. Finally, the final approximate solutions were obtained and simulation results were generated from the general solution graphically.Item The Algebraic Structure of an Implicit Runge- Kutta Type Method(International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2024-11) Raihanatu Muhammad; Abdulmalik OyedejiIn this paper, the theory of linear transformation (Homomorphism) and monomorphism is applied to a first-order Runge-Kutta Type Method illustrated in a Butcher Table and the extended second order Runge- Runge-Kutta type Method to substantiate their uniform order and error constants obtained. A homomorphism is a mapping from one group to another group which preserves the group operations. It’s sometimes called the operation preserving function. The methods which initially are Linear Multistep were reformulated into Runge-Kutta (R-K) Type to establish the advantages the R-K has over Linear Multistep. The first-order Linear multistep was reformulated into first-order R-K type which was further extended to second order. This extension can be made to higher order. For this study, the extension was limited to the second order.