Browsing by Author "A.S Abdulkareem"

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    Error and Convergence Analysis of a Hybrid Runge- Kutta Type Method
    (International Journal of Science and Technology Publications UK, 2015-04) Muhammad R; Y. A Yahaya,; A.S Abdulkareem
    Implicit Runge- Kutta methods are used for solving stiff problems which mostly arise in real life problems. Convergence analysis helps us to determine an effective Runge- Kutta Method (RKM) to use, but due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation. In this paper, we derived a hybrid Runge -Kutta Type method (RKTM) for 𝑘=1, obtained the order and error constant and convergence analysis of the method.
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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).