Mathematics

Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/100

Mathematics

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Start date: 2011Subject: search.filters.subject.Implicit

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    REFORMULATION OF TWO STEP IMPLICIT LINEAR MULTI-STEP BLOCK HYBRID METHOD INTO RUNGE KUTTA TYPE METHOD FOR THE SOLUTION OF SECOND ORDER INITIAL VALUE PROBLEM (IVP)
    (2025) ALIYU Abubakar; MUHAMMAD Raihanatu; ABDULHAKEEM Yusuf
    Second-order ordinary differential equations (ODEs) is unavoidable in scientific and engineering fields. This research focuses on the reformulation of two-step implicit linear multistep block hybrid method into a seven-stage Runge-Kutta type method for the solution of second-order initial value problems (IVPs). A two-step, four-off-grid-point implicit block hybrid collocation method for first-order initial value problems was derived. Its order and error constants were determined, which shows that the schemes were of order 8, 8, 8, 8, 8 and 9 with respective error constants of , , , , . The derived block method was reformulated into a seven-stage Runge-Kutta type method (RKTM) for the solution of first-order ordinary differential equations; this reformulation was extended to handle the required second-order ordinary differential equations. The second-order Runge- Kutta-type method derived was implemented on numerical experiments. The method was found to be better than existing methods in the literature.
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    The Algebraic Structure of an Implicit Runge- Kutta Type Method
    (International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2024-11) Raihanatu Muhammad; Abdulmalik Oyedeji
    In this paper, the theory of linear transformation (Homomorphism) and monomorphism is applied to a first-order Runge-Kutta Type Method illustrated in a Butcher Table and the extended second order Runge- Runge-Kutta type Method to substantiate their uniform order and error constants obtained. A homomorphism is a mapping from one group to another group which preserves the group operations. It’s sometimes called the operation preserving function. The methods which initially are Linear Multistep were reformulated into Runge-Kutta (R-K) Type to establish the advantages the R-K has over Linear Multistep. The first-order Linear multistep was reformulated into first-order R-K type which was further extended to second order. This extension can be made to higher order. For this study, the extension was limited to the second order.
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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.
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    Reformulation of Block Implicit Linear Multistep Method into Runge Kutta Type Method for Initial Value Problem
    (International Journal of Science and Technology Publications UK, 2015-04) Muhammad R; Y.A Yahaya; A.S. Abdulkareem
    In this research work, we reformulated the block hybrid Backward Differentiation Formula (BDF) for 𝑘=4 into Runge Kutta Type Method (RKTM) of the same step number for the solution of Initial value problem in Ordinary Differential Equation (ODE). The method can be use to solve both first and second order (special or general form). It can also be extended to solve higher order ODE. This method differs from conventional BDF as derivation is done only once