Browsing by Author "K. Issa"

Now showing 1 - 16 of 16
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    A GENERALIZED SCHEME FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS BY THE RECURSIVE FORMULATION OF TAU METHOD
    (2013-05) K. Issa; R.B. Adeniyi
    The generalization of the recursive form of the tau method for both overdetermined and non-overdetermined ordinary differential equations of the initial value type is the main thrust of the work reported here. This will facilitate an automation of this variant of the method and consequently an efficient utilization of the technique. Results from the numerical experiment confirm the validity and effectiveness of the derived scheme.
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    An analogue of the tau method for ordinary differential equation
    (2010) K. Issa; R. B. Adeniyi
    In this paper, we construct three orthogonal polynomials which are incorporated into the perturbation term of a numerical scheme analogue to the Ortiz recursive formulation of the Lanczos tau method. The method was implemented on some selected problems and the accuracy obtained justifies the desirability of the numerical scheme.
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    Approximate Solution of Perturbed Volterra-Fredholm Integrodifferential Equations by Chebyshev-Galerkin Method
    (Hindawi, 2017-01-12) K. Issa; F. Salehi
    In this work, we obtain the approximate solution for the integrodifferential equations by adding perturbation terms to the right hand side of integrodifferential equation and then solve the resulting equation using Chebyshev-Galerkin method. Details of the method are presented and some numerical results along with absolute errors are given to clarify the method. Where necessary, we made comparison with the results obtained previously in the literature. The results obtained reveal the accuracy of the method presented in this study.
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    Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics
    (Nigerian Society of Physical Sciences, 2024-05-31) K. Issa; R. A. Bello; M. H. Sulaiman
    In this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter α = 1 and varying the values of γ, ψ, and τ. These three equations were derived from the general non-linear dynamical wave equations when the constants therein assumed certain specific values. Obviously, from the tabulated results, we observed that the approximate solution for each example compares favourably with the existing results in the literature; therefore, the proposed scheme is effective and accurate in solving Allen-Cahn, Newell-Whitehead, and Fisher equations. All the computational work was done using Mathematica, and all the graphs were plotted using MATLAB.
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    Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics
    (2024) K. Issa; R. A. Bello; M. H. Sulaiman
    In this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter \alpha = 1 and varying the values of \gamma, \phi, and \tau. These three equations were derived from the general non-linear dynamical wave equations when the constants therein assumed certain specific values. Obviously, from the tabulated results, we observed that the approximate solution for each example compares favourably with the existing results in the literature; therefore, the proposed scheme is effective and accurate in solving Allen-Cahn, Newell-Whitehead, and Fisher equations. All the computational work was done using Mathematica, and all the graphs were plotted using MATLAB.
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    Approximate Solutionof Space Fractional Order Difusion Equation
    (Journal of the Nigerian Society of Physical Sciences (JNSPS), 2023-05) K. Issa; A.S. Olorunnisola; T.O. Aliu; A.D. Adeshola
    J. Nig. Soc. Phys. Sci. 5 (2023) 1368 Journal of the Nigerian Society of Physical Sciences Approximate solution of space fractional order diffusion equations by Gegenbauer collocation and compact finite difference scheme K. Issa∗, A. S. Olorunnisola, T. O. Aliu, A. D. Adeshola Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria. Abstract In this paper, approximation of space fractional order diffusion equation are considered using compact finite difference technique to discretize the time derivative, which was then approximated via shifted Gegenbauer polynomials using zeros of (N − 1) degree shifted Gegenbauer polynomial as collocation points. The important feature in this approach is that it reduces the problems to algebraic linear system of equations together with the boundary conditions gives (N + 1) linear equations. Some theorems are given to establish the convergence and the stability of the proposed method. To validate the efficiency and the accuracy of the method, obtained results are compared with the existing results in the literature. The graphical representation are also displayed for various values of β− Gegenbauer polynomials. It can be observe in the tables of the results and figures that the proposed method performs better than the existing one in the literature
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    Comparison of some numerical methods for the solution of fourth order integro-differential equations
    (2014-11) A. K. Jimoh; K. Issa
    The numerical methods for solving fourth order integro-differential equations are presented. The methods are based on replacement of the unknown function by power series and Legendre polynomials of appropriate degree. The proposed methods convert the resulting equation by some examples considered show that the standard collocation method proved superior to the perturbed collocation method. Two examples are considered to illustrate the efficiency and accuracy of the methods.
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    Computational error estimate for the power series solution of ODEs using zeros of Chebyshev polynomial
    (Journal of Nigerian Association of Mathematical Physics, 2015-05) K. Issa; G. R. Ibrahim; G. N. Bakare
    This paper compared the error estimation of power series solution with the recursive tau method for solving ordinary differential equations. From the computational viewpoint, the power series using zeros of Chebyshev polynomial is effective, accurate and easy to use.
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    Corner Rules Method of Solving Transportation Problem
    (Earthline, 2022-07-07) T.O. Aliu; Y.O. Aderinto; K. Issa
    Several approaches have been advanced for solving transportation problems. The most prominent of them in various text being, North West Corner Rule(NWCR), Least Cost Method(LCM), and Vogel's Approximation Method(VAM). This paper considered three additional corner rules, which are North East Corner Rule(NECR), South West Corner Rule(SWCR) and South East Corner Rule(SECR). Algorithms ware provided for obtaining initial feasible solution to Transportation Problems. Three test examples were considered using the rules. The results revealed that the NECR and SWCR have equal result. While NWCR and SECR also produce the same result. NECR and SWCR however, better minimize transportation cost. The two methods are therefore recommended for use in any business organization requiring shipment of products.
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    Corner Rules Method of Solving Transportation Problem
    (Earthline Publishers, 2022-07-07) T.O. Aliu; Y.O. Aderinto; K. Issa
    Several approaches have been advanced for solving transportation problems. The most prominent of them in various text being, North West Corner Rule(NWCR), Least Cost Method(LCM), and Vogel's Approximation Method(VAM). This paper considered three additional corner rules, which are North East Corner Rule(NECR), South West Corner Rule(SWCR) and South East Corner Rule(SECR). Algorithms ware provided for obtaining initial feasible solution to Transportation Problems. Three test examples were considered using the rules. The results revealed that the NECR and SWCR have equal result. While NWCR and SECR also produce the same result. NECR and SWCR however, better minimize transportation cost. The two methods are therefore recommended for use in any business organization requiring shipment of products.
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    Extension of generalized recursive Tau method to non-linear ordinary differential equations
    (Elsevier Ltd, 2016) K. Issa; R.B. Adeniyi
    In a recent paper, we reported a generalized approximation technique for the recursive formulation of the Tau method. This paper is concerned with an extension of that discourse to non-linear ordinary differential equations. The numerical results show that the method is effective and accurate.
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    Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method
    (2014-04-14) W.A. Yahya; K. Issa; B.J. Falaye; K.J. Oyewumi
    We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.
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    Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method
    (2014) W.A. Yahya; K. Issa; B.J. Falaye; K.J. Oyewumi
    We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.
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    Perturbed Galerkin Method for Solving Integro- Differential Equations
    (Hindawi, 0002-04-15) K. Issa; J.Biazar; T.O. Agboola; T. Aliu
    In this paper, perturbed Galerkin method is proposed to find numerical solution of an integro-differential equations using fourth kind shifted Chebyshev polynomials as ba- sis functions which transform the integro-differential equation into a system of linear equations. The system of linear equations are then solved to obtain the approximate solution. Examples to justify the effectiveness and accuracy of the method are pre- sented and their numerical results are compared with Galerkin’s method, Taylor’s series method and Tau’s method which provide validation for the proposed approach. The errors obtained justify the effectiveness and accuracy of the method.
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    Perturbed Galerkin Method for Solving Integro-Differential Equations
    (Hindawi, 2022-04-15) K. Issa; J. Biazar; T. O. Agboola; T. Aliu; Saeid Abbasbandy
    In this paper, perturbed Galerkin method is proposed to find numerical solution of an integro-differential equations using fourth kind shifted Chebyshev polynomials as basis functions which transform the integro-differential equation into a system of linear equations. The systems of linear equations are then solved to obtain the approximate solution. Examples to justify the effectiveness and accuracy of the method are presented and their numerical results are compared with Galerkin’s method, Taylor’s series method, and Tau’s method which provide validation for the proposed approach. The errors obtained justify the effectiveness and accuracy of the method.
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    Thermal management of radiation mechanism over a stretchable curved surface inside the circle: performance enhancement of molybdenum disulfide and silicon dioxide hybrid nanofluid for thermal technology advancement
    (2024) A. M. Obalalu; Adil Darvesh; L. O. Aselebe; S. O. Salawu; K. Issa
    The main perspective of this research focuses on addressing the pressing industry problem related to energy inefficiency by studying the heat transfer improvement of solar radiative and heat absorption/emission phenomena over a stretchable curved sheet inside the circle. To increase the model novelty, the combined influence of thermal relaxation, Newtonian heating, radiation mechanism, and Darcy-Forchheimer are included in the problem formulation of governing equations. Furthermore, this research employs the Cattaneo–Christov heat theory model to investigate the thermal flux via utilising the abovementioned phenomenon with the purpose of advancing thermal technology. In this perspective, Molybdenumdisulfide (MoS2) with a base fluid of Propylene glycol (C3H8O2) is utilised as nanoparticles for nanofluid (NFs), and for making hybrid nanofluid (HNFs), Molybdenum disulfide (MoS2) and silicon dioxide (SiO2)are utilised with of Propylene glycol (C3H8O2). The equations are converted into ordinary Differential equations using Similarity variables. Shifted Legendre collocation scheme (SLCS) is then utilised to solve the simulation of the modelled equations. The findings show that the solar radiation effects boosted the heating performance of the MoS2 − SiO2/ C3H8O2 hybrid nanofluid.