Browsing by Author "Y. A. Yahaya"

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    AN ANALYSIS OF ALGEBRAIC PATTERN OF A FIRST ORDER AND AN EXTENDED SECOND ORDER RUNGE-KUTTA TYPE METHOD
    (Faculty of Science, Kaduna State University, 2020) R. Muhammad,; Y. A. Yahaya; A.S. Abdulkareem
    The algebraic pattern of a 6-Stage Block Hybrid Runge –Kutta Type Methods (BHRKTM) for the solution of Ordinary Differential Equations (ODEs) is carefully analyzed. The analysis of the methods expressed in the Butcher Tableau led to the evolvement of two equations that satisfy the Runge – Kutta consistency conditions. The reason behind the uniform order and error constant for the developed first order and extended second order methods is explained using the theory of linear transformation and monomorphism. The pattern was retained during the transformation.
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    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. Abdulkareem
    In 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.