Browsing by Author "Abdulhakeem Yusuf"

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    A Mathematical Study of Contaminant Transport with First-order Decay and Time-dependent Source Concentration in an Aquifer
    (Universal Journal of Applied Mathematics, 2013-12-10) Rasaq O. Olayiwola; JIMOH, OMANANYI RAZAQ; Abdulhakeem Yusuf; Samuel Abubakar
    A mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.
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    METHOD INTO RUNGE KUTTA TYPE METHOD FOR FIRST ORDER INITIAL VALUE PROBLEM (IVP)
    (2025-03) Abubakar Aliyu; Raihanatu Muhammad; Abdulhakeem Yusuf
    Problems 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 stable