Mathematics - Scholarly Publications

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Browsing Mathematics - Scholarly Publications by Author "Akinfenwa, O.A."

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  • Item
    Open Access
    A family of Continuous Third Derivative Block Methods for solving stiff systems of first order ordinary differential equations
    (Elsevier, 2015-06) Akinfenwa, O.A.; Akinnukawe, B.; Mudasiru, S.B.
    This paper presents a family of Continuous Third Derivative Block Methods (CTDBM) of order k + 3 for the solution of stiff systems of ordinary differential equations. The approach uses the collocation and interpolation technique to generate the main Continuous Third Derivative method (CTDM) which is then used to obtain the additional methods that are combined as a single block methods. Analysis of the methods show that the method is L-stable up to order eight. Numerical examples are given to illustrate the accuracy and efficiency of the proposed method.
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    Open Access
    HYBRID BLOCK ALGORITHM FOR SOLVING DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH HESSENBERG INDEX 3
    (2019-04) Akinnukawe, B.I.; Akinfenwa, O.A.; Okunuga, S.A.
    Higher-Index Differential-Algebraic Equations (DAEs) are known to be numerically and analytically difficult to solve. In this paper, an hybrid block integrator of order seven is proposed for the solution of Hessenberg DAEs of Index-3. This is achieved by constructing a continuous hybrid second derivative method used to obtain the main and additional methods which are combined to form a single block method that simultaneously provide the approximate solutions to the DAEs. The stability analysis of the derived block integrator is discussed. Two test problems are solved to demonstrate the efficiency of the method.
  • Item
    Open Access
    L-Stable Block Backward Differentiation Formula for Parabolic Partial Differential Equations
    (Elsevier, 2016) Akinnukawe, B.I.; Akinfenwa, O.A.; Okunuga, S.A.
    In this paper, an L-stable Second Derivative Block Backward Differentiation Formula (SDBBDF) of order 5 is presented for the solutions of parabolic equations. It applied the use of the classical method of lines for the discretization of the parabolic equations. The method reduces the one-dimensional parabolic partial differential equation which has integral or non-integral boundary conditions to a system of Ordinary Differential Equations (ODEs) with initial conditions. The stability properties of the block method are investigated using the boundary locus plot and the method was found to be L-stable. The derived method is implemented on standard problems of parabolic equations and the results obtained show that the method is accurate and efficient.