Mathematics
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Mathematics
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Item A TWO POINT BLOCK HYBRID METHOD FOR SOLVING STIFF INITIAL VALUE PROBLEMS(JOURNAL OF MATHEMATICAL SCIENCES, 2011) Muhammad RIn this paper, a self starting hybrid method of order (3, 3,3) is proposed for the solution of stiff initial value problem of the form y' = f(x.y). The continous formation of the integrator enables us to differentiate and evaluate at grid and off grid points. The schemes compared favourably with exact results and results from Okunuga (2008)Item Reformulation of Block Implicit Linear Multistep Method into Runge Kutta Type Method for Initial Value Problem(International Journal of Science and Technology Publications UK, 2015-04) Muhammad R; Y.A Yahaya; A.S. AbdulkareemIn this research work, we reformulated the block hybrid Backward Differentiation Formula (BDF) for 𝑘=4 into Runge Kutta Type Method (RKTM) of the same step number for the solution of Initial value problem in Ordinary Differential Equation (ODE). The method can be use to solve both first and second order (special or general form). It can also be extended to solve higher order ODE. This method differs from conventional BDF as derivation is done only onceItem INFLUENCE OF ZERO-ORDER SOURCE AND DECAY COEFFICIENTS ON THE CONCENTRATION OF CONTAMINANTS IN TWO-DIMENSIONAL CONTAMINANT FLOW(SCHOOL OF PHYSICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA, 2017-04-23) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.; Bolarin, G. A.In this article, an eigenfunctions expansion method is used in studying the behavior of two-dimensional contaminant flow problem with non-zero initial concentration. The mathematical model describing the contaminant flow is described by advection, dispersion, adsorption, first order decay and zero-order source. It is assumed that the adsorption term is modeled by Freudlich isotherm. Before the application of the eigenfunctions method, the parameter expanding method is applied on the model and the boundary conditions are transformed to the homogeneous type. Thereafter, the approximate solution of the resulting initial value problem was obtained successively. The results obtained are expressed graphically to show the effect of change in the zero-order source and decay coefficients on the concentration of the contaminants. From the analysis of the results, it was discovered that the contaminant concentration decreases with increase in the distance from the origin as the zero-order source and decay coefficient increases.Item A MATHEMATICAL MODEL OF YELLOW FEVER DISEASE DYNAMICS INCORPORATING SPECIAL SATURATION INTERACTIONS FUNCTIONS(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Akinwande, N. I.; Abdulrahman, S.; Ashezua, T. T.; Somma, Samuel AbuWe proposed an Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Process functions, obtained the equilibrium states of the model equations and analyzed same for stability. Conditions for the elimination of the disease in the population are obtained as constraint inequalities on the parameters using the basic reproduction number 0 R demographic and epidemiological data. . Graphical simulations are presented using someItem SENSITIVITY ANALYSIS FOR THE MATHEMATICAL MODELING OF MEASLES DISEASE INCORPORATING TEMPORARY PASSIVE IMMUNITY(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Somma, Samuel Abu; Akinwande, N. I.Measles is an airborne disease which spreads easily through the coughs and sneezes of those infected. Measles antibodies are transferred from mothers who have been vaccinated against measles or have been previously infected with measles to their newborn children. These antibodies are transferred in low amounts and usually last six months or less. In this paper a mathematical model of measles disease was formulated incorporating temporary passive immunity. There exist two equilibria in the model; Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The Disease Free Equilibrium (DFE) state was analyzed for local and global stability. The Basic Reproduction Number 0 R was computed and used to carried out the sensitivity analysis with some parameters of the mode. The analysis shows that as contact rate increases the 0 as the vaccination rate v increases the 0 R decreases. Sensitive parameters with the R R 0 increases and were presented graphically. The disease will die out of the population if the attention is given to high level immunization.Item A Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Interactions Functions(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Akinwande, N. I.; Abdulrahman, S.; Ashezua, T. T.; Somma, Samuel AbuWe proposed an Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Process functions, obtained the equilibrium states of the model equations and analyzed same for stability. Conditions for the elimination of the disease in the population are obtained as constraint inequalities on the parameters using the basic reproduction number 0R . Graphical simulations are presented using some demographic and epidemiological data.Item Local Stability Analysis of a Tuberculosis Model incorporating Extensive Drug Resistant Subgroup(Pacific Journal of Science and Technology, 2017-05-25) Eguda, F. Y.; Akinwande, N. I.; Abdulrahman, S.; Kuta, F. A.; Somma, Samuel AbuThis paper proposes a mathematical model for the transmission dynamics of Tuberculosis incorporating extensive drug resistant subgroup. The effective reproduction number c R was obtained and conditions for local stability of the disease free equilibrium and endemic equilibrium states were established. Numerical simulations confirmed the stability analysis and further revealed that unless proper measures are taken against typical TB, progression to XDR-TB, mortality and morbidity of infected individuals shall continue to rise.Item Local Stability Analysis of a River Blindness Disease Model with Control(Pacific Journal of Science and Technology., 2018-05-12) Oguntolu, F. A.; Bolarin, G. A.; Somma, Samuel Abu; Bello, A. O.In this paper, a mathematical model to study the dynamics of River Blindness is presented. The existence and uniqueness of solutions of the model were examined by actual solution. The effective reproduction number was obtained using the next generation matrix. The Disease Free Equilibrium (DFE) State was obtained and analysed for stability. It was found that, the DFE State is Locally Asymptotically Stable (LAS) if the effective unstable if reproduction number R 0 1 .Item Mathematical Modelling for the Effect of Malaria on the Heterozygous and Homozygous Genes(6th International Conference on Mathematical Analysis and Optimization: Theory and Applications (ICAPTA 2019), 2019-03-29) Abdurrahman, N. O.; Akinwande, N. I.; Somma, Samuel AbuThis paper models the effect of malaria on the homozygous for the normal gene (AA), heterozygous for sickle cell gene (AS) and homozygous for sickle cell gene (SS) using the first order ordinary differential equation. The Diseases Free Equilibrium (DFE) was obtained and used to compute the basic reproduction Number Ro. The local stability of the (DFE) was analyzed.Item Differential Transformation Method (DTM) for Solving Mathematical Modelling of Monkey Pox Virus Incorporating Quarantine(Proceedings of 2nd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2019-06-26) Somma, Samuel Abu; Akinwande, N. I.; Abdurrahman, N. O.; Zhiri, A. B.In this paper the Mathematical Modelling of Monkey Pox Virus Incorporating Quarantine was solved semi-analytically using Differential Transformation Method (DTM). The solutions of difference cases were presented graphically. The graphical solutions gave better understanding of the dynamics of Monkey pox virus, it was shown that effective Public Enlightenment Campaign and Progression Rate of Quarantine are important parameters that will prevent and control the spread of Monkey Pox in the population.Item Agreement between the Homotopy Perturbation Method and Variation Iterational Method on the Analysis of One-Dimensional Flow Incorporating First Order Decay(SCHOOL OF PHYSICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA, 2019-06-28) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.In this paper, a comparative study of reactive contaminant flow for constant initial concentration in one dimension is presented. The adsorption term is modeled by Freudlich Isotherm. An approximation of the one-dimensional contaminant flow model was obtained using homotopy-perturbation transformation and the resulting linear equations were solved semi-analytically by homotopyperturbation method (HPM) and Variational Iteration Method (VIM). Graphs were plotted using the solution obtained from the methods and the results presented and discussed. The analysis of the results obtained show that the concentration of the contaminant decreases with time and distance as it moves away from the origin.Item Local and Global Stability Analysis of a Mathematical Model of Measles Incorporating Maternally-Derived-Immunity(Proceedings of International Conference on Applied Mathematics & Computational Sciences (ICAMCS),, 2019-10-19) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.In this paper, the local stabilities of both the Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) were analyzed using the Jacobian matrix stability technique. The global stabilities were analyzed using Lyapunov function. The analysis shows that the DFE is locally and globally stable if the basic reproduction number R 0 1 R 0 1 and R 0 1 respectively. The EE is also locally and globally stable if . Vaccination and recovery rates have been shown from the graphical presentation as the important parameter that will eradicate measles from the population.Item The Pollutant Concentration Regime in a Flow due to Variable Time-Dependent Off-Diagonal Dispersion(AIJR Publisher, 2019-10-19) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.In this paper, an Eigen Functions expansion technique was used to obtain an analytical solution of twodimensional contaminant flow problem with non-zero initial concentration. The equation which describes the two-dimensional contaminant flow model is a partial differential equation characterized by advection, dispersion, adsorption, first order decay and zero-order source. It was assumed that the adsorption term was modeled by Freudlich isotherm. The off-diagonal dispersion parameter was incorporated into the two-dimensional contaminant model in order to expand the scope of the analysis. The model equation was non-dimensionalized before the parameter expanding method was applied. The resulting equations were solved successively by Eigen functions expansion technique. This research establishes that the pollutant concentration declines with increase in distances in both directions as the off-diagonal dispersion coefficient, zero-order source coefficient and vertical dispersion coefficient increases.Item Mathematical Modeling of Algae Population Dynamics on the Surface of Water(2019-11-12) Abdurrahman, O. N.; Akinwande, N. I.; Somma, Samuel AbuThe paper presented an analytical solution of the exponential growth model of algae population dynamics on the water surface. The Computer Symbolic Algebraic Package, MAPLE is used to simulate the graphical profiles of the population with time while varying the parameters, such as diffusion and rate of change of algae density, governing the subsistence or extinction of the water organisms.Item Extended Block Hybrid Backward Differentiation Formula for Second Order Fuzzy Differential Equations Using Legendre Polynomial as Basis Function.(Federal University of Technology, Minna, Nigeria, 2020-03-12) Ma’ali, A. I.,; Mohammed, U.; Khadeejah James Audu; Yusuf, A.; Abubakar, A. D.In this paper, we developed an implicit continuous four-step Extended Block Hybrid Backward Differentiation Formulae (EBHBDF) for the direct solution of Fuzzy Differential Equations (FDEs). For this purpose, the Legendre polynomial was employed as the basis function for the development of schemes in a collocation and interpolation techniques. in this regard and the results are satisfied the convex triangular fuzzy number. We also compare the numerical results with the exact solution, and it shows that the proposed method is good approximation for the analytic solution of the given second order Fuzzy Differential EquationsItem An Implicit Runge-Kutta Type Method for the Solution of Initial Value Problems(KASU JOURNAL OF MATHEMATICAL SCIENCES, 2020-06) R. Muhammad; Y. A. Yahaya; A. S. AbdulkareemIn this research paper, an implicit block hybrid Backward Differentiation Formula (BDF) for 𝑘=2 is reformulated into a Runge-Kutta Type Method (RKTM) of the same step number. The method can be used to solve both first and second order (special or general form) initial value problem in Ordinary Differential Equation (ODE). This method differs from conventional BDF as derivation is done only once. It can also be extended to solve higher order ODE.Item Improving Accuracy Through the Three Steps Block Methods For Direct Solution of Second Order Initial Value Problem Using Interpolation and Collocation Approach(KASU JOURNAL OF MATHEMATICAL SCIENCES (KJMS), 2020-06) R. Muhammad; I. D. ZakariyauThis paper presents three-step block method for direct solution of second order initial value problems of ordinary differential equations. The collocation and interpolation approach was adopted to generate a continuous block method using power series as basis function. The properties of the proposed approach such as order, error constant, zero-stability, consistency and convergence were also investigated. The proposed method competes favorably with exact solution and the existing methods.Item Stability Analysis for Mathematical Modeling of Dengue Fever Transmission and Control(Proceedings of International Conference on Contemporary Developments in Mathematical Sciences (ICCDMS), 2021-04-13) Aliyu, A. H.; Akinwande, N. I.; Somma Samuel AbuDengue fever is one of the greatest health challenges in the present world. In this work, mathematical modeling of dengue fever transmission and control was formulated. The model considered the human population h N and the vector population m N which are further subdivided into six classes, susceptible human 𝑆, infected human 𝐼, temporary recovered human class 1 R, permanently recovered human class 2 R , susceptible mosquito 1 M, and infected mosquito class 2 M . The Disease Free Equilibrium (DFE) point was obtained and the basic Reproduction number 0 R was computed. The Disease Free Equilibrium (DFE) is locally and globally asymptotically stable when 1 0 R .Item Stability Analysis for Mathematical Modeling of Dengue Fever Transmission and Control(Proceedings of International Conference on Contemporary Developments in Mathematical Sciences (ICCDMS), 2021-04-13) Aliyu, A. H.; Akinwande, N. I.; Somma, Samuel AbuDengue fever is one of the greatest health challenges in the present world. In this work, mathematical modeling of dengue fever transmission and control was formulated. The model considered the human population h N and the vector population m N which are further subdivided into six classes, susceptible human 𝑆, infected human 𝐼, temporary recovered human class 1 R , permanently recovered human class 2 R , susceptible mosquito 1 M , and infected mosquito class 2 M . The Disease Free Equilibrium (DFE) point was obtained and the basic Reproduction number 0 R was computed. The Disease Free Equilibrium (DFE) is locally and globally asymptotically stable when R0 1.Item Refinement of Triple Accelerated Over Relaxation (RTAOR) Method for Solution of Linear System(Nigeria Mathematical Sciences (NMS), 2021-04-21) Khaddejah James Audu; Yahaya, Y. A.; Adeboye, K. R; Abubakar, U. YIn this paper, a Refinement of Extended Accelerated Over-Relaxation (REAOR) iterative method for solving linear systems is presented. The method is designed to solve problems of partial differential equations that results into linear systems having coefficient matrices such as weak irreducible diagonally dominant matrix and 𝐿−matrix (or 𝑀−matrix). Sufficient criterion for convergence are examined and few numerical illustrations are considered to ascertain efficiency of the new method. Outcome of the numerical results reveals that the REAOR iterative method is more efficient when compared with Extended Accelerated Over-Relaxation iterative method in terms of computational time, level of accuracy and required number of iterations for convergence
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