Mathematics

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Mathematics

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Author: search.filters.author.Muhammad RHas files: Yes

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    A TWO POINT BLOCK HYBRID METHOD FOR SOLVING STIFF INITIAL VALUE PROBLEMS
    (JOURNAL OF MATHEMATICAL SCIENCES, 2011) Muhammad R
    In this paper, a self starting hybrid method of order (3, 3,3) is proposed for the solution of stiff initial value problem of the form y' = f(x.y). The continous formation of the integrator enables us to differentiate and evaluate at grid and off grid points. The schemes compared favourably with exact results and results from Okunuga (2008)
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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
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    A 4-Step Order (K + 1) Block Hybrid Backward Differentiation Formulae (BHBDF) for the Solution of General Second Order Ordinary Differential Equations
    (2023-12) Muhammad R; Hussaini A
    In this paper, the block hybrid backward differentiation formulae (BHBDF) for the step number 𝑘 = 4 was developed using power series as basis function for the solution of general second order ordinary differential equation. The idea of interpolation and collocation of the power series at some selected grid and off- grid points gave rise to continuous schemes which were further evaluated at those points to produce discrete schemes combined together to form block methods. Numerical problems were solved with the proposed methods and were found to perform effectively.