Browsing by Author "Muhammad Raihanatu"

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    4-Step Block Hybrid Backward Differentiation Formula For Solving Second Order (BHBDF II) Ordinary Differential Equations
    (2024) Hussaini Hajarat; Muhammad Raihanatu; Yusuf Abdulhakeem
    This research work presents the derivation and implementation of a 4-step linear multistep method of block hybrid backward differentiation formula for solving nonlinear second-order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the proposed numerical scheme where the legendary polynomial is adopted as a basic function. The 4-step BHBDF has higher order of accuracy p = 11 which implies that it is consistent. The proposed numerical block method is further applied to finding direct solution to nonlinear second order ordinary differentiation equations. This implementation strategy is more accurate than some existing methods considered in the literature.
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    A 3-step block hybrid backward differentiation formulae (bhbdf) for the solution of general second order ordinary differential equation
    (New Trends in Mathematical Sciences, 2021-07-12) Hussaini Alhassan; Muhammad Raihanatu
    In this paper, the block hybrid Backward Differentiation formulae (BHBDF) for the step number k=3 is 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.