Mathematics

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Mathematics

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Start date: 2013Subject: search.filters.subject.Hybrid

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    Formulation Of A Standard Runge- Kutta Type Method For The Solution First And Second Order Initial Value Problems
    (Researchjournali’s Journal of Mathematics, 2015-03) Muhammad R.; Y. A Yahaya; A.S Abdulkareem
    In this paper, we present a standard Runge-Kutta Type Method (RKTM) for . The process produces Backward Differentiation Formula (BDF) scheme and its hybrid form which combined together to form a block method. The method is reformulated into a Runge-Kutta Type of the same step number for the solution of first and second order (special or general) initial value problem of Ordinary Differential Equation (ODE).
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    DERIVATION AND ANALYSIS OF BLOCK IMPLICIT HYBRID BACKWARD DIFFERENTIATION FORMULAE FOR STIFF PROBLEMS
    (Nigerian Journal of Mathematics and Applications, 2014) MUHAMMAD, R.; YAHAYA, Y. A.; IDRIS L.
    The Hybrid Backward Di erentiation Formula (HBDF) for the case k = 3 was reformulated into continuous form using the idea of multistep collocation. The continuous form was evaluated at some grid and o grid points which gave rise to discrete schemes employed as block methods for direct solution of rst order Ordinary Di erential Equation y0 = f(x; y). The requirement of a starting value and the overlap of solution model which are associated with conventional Linear Multistep Methods were eliminated by this approach. A convergence analysis of the derived hybrid schemes to establish their e ec- tiveness and reliability is presented. Numerical example carried out on sti problem further substantiates their performance.