Mathematics - Scholarly Publications

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Browsing Mathematics - Scholarly Publications by Author "Akinnukawe, B.I."

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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.
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    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.
  • Item
    Open Access
    A Seventh-order Block Integrator for Solving Stiff Systems
    (2015) Akinnukawe, B.I.; Okunuga, S.A.
    In this paper, an L_0- stable Second Derivative Block Integrator of uniform order seven is proposed for the numerical integration of stiff systems, including large stiff systems resulting from semi-discretization of Parabolic differential equations. The conventional 3-step second derivative backward differentiation formula is obtained from a continuous scheme while the additional methods are obtained from the second derivative of the same continuous scheme. All methods are derived via Interpolation and Collocation techniques and assembled into a block scheme. The convergence and stability properties of the block scheme are discussed and the stability region shown. The performance of the scheme as compared to other existing schemes is considered favorable.