Mathematics

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

Mathematics

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Start date: 2020Subject: search.filters.subject.collocation

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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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    Improving Accuracy Through the Three Steps Block Methods For Direct Solution of Second Order Initial Value Problem Using Interpolation and Collocation Approach
    (KASU JOURNAL OF MATHEMATICAL SCIENCES (KJMS), 2020-06) R. Muhammad; I. D. Zakariyau
    This paper presents three-step block method for direct solution of second order initial value problems of ordinary differential equations. The collocation and interpolation approach was adopted to generate a continuous block method using power series as basis function. The properties of the proposed approach such as order, error constant, zero-stability, consistency and convergence were also investigated. The proposed method competes favorably with exact solution and the existing methods.