Browsing by Author "Yahaya, Y. A."

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BLOCK METHOD APPROACH FOR COMPUTATION OF ERRORS OF SOME ADAMS CLASS OF METHODS
(Association of Nigerian Journal of Physics, 2022-12-12) Yahaya, Y. A.; Odeyemi, A. O.; Khadeejah James Audu
Traditionally, the error and order constant of block linear multistep methods were analyzed by examining each block members separately. This paper proposes a block-by-block analysis of the schemes as they appear for implementation. Specifically, cases when k= 2, 3, 4, and 5 for Adams Moulton (implicit) are reformulated as continuous schemes in order to generate a sufficient number of schemes required for the methods to be self-starting. The derivation was accomplished through the continuous collocation technique utilizing power series as the basis function, and the property of order and error constants is examined across the entire block for each case of the considered step number. The findings of the study generated error constants in block form for Adams Bashforth and Adams Moulton procedures at steps 2, 3, 4, 5 k  . Furthermore, the relevance of the study demonstrates that calculating all members' error constants at once, reduces the amount of time necessary to run the analysis. The new approach, for examining the order and error constants of a block linear multistep method, is highly recommended for application in solving real-world problems, modelled as ordinary and partial differential equations
EXTENDED ACCELERATED OVER-RELAXATION (EAOR) METHOD FOR SOLUTION OF A LARGE AND SPARSELINEAR SYSTEMS
(Federal University of Technology, Minna, Nigeria, 2021-06-14) Khadeejah James Audu; Yahaya, Y. A.; Adeboye, K. R.; Abubakar, U. Y.
In this research, we introduce a stationary iterative method called Extended Accelerated Over Relaxation (EAOR) method for solving linear systems. The method, an extension of the Accelerated Over Relaxation (A OR) method, was derived through the interpolation procedure with respect to the sub-matrices in application of a genera/ linear stationary schemes. We studied the convergence properties of the method for special matrices such as L-, H- and irreducible diagonally dominant matrices and proposed some convergence theorems. Some numerical tests were carried out to test the efficiency of the proposed method with existing methods in terms of number of iterations, spectral radius and computational time. The results revealed the superiority of the proposed EAOR method over the AOR method in terms of convergence rate.
Refinement of Extended Accelerated Over Relaxation method for solution of linear systems.
(Benue State University, Makurdi, Nigeria, 2021-09-22) Khadeejah James Audu; Yahaya, Y. A.; Adeboye, K. R.; Abubakar, U. Y.
Given any linear stationary iterative methods in the form 𝑧(𝑖+1) = 𝐽𝑧(𝑖) + 𝑓, where 𝐽 is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form 𝐴𝑧 = 𝑏. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.
Refinement of Triple Accelerated Over Relaxation (RTAOR) Method for Solution of Linear System
(Nigeria Mathematical Sciences (NMS), 2021-04-21) Khaddejah James Audu; Yahaya, Y. A.; Adeboye, K. R; Abubakar, U. Y
In this paper, a Refinement of Extended Accelerated Over-Relaxation (REAOR) iterative method for solving linear systems is presented. The method is designed to solve problems of partial differential equations that results into linear systems having coefficient matrices such as weak irreducible diagonally dominant matrix and 𝐿−matrix (or 𝑀−matrix). Sufficient criterion for convergence are examined and few numerical illustrations are considered to ascertain efficiency of the new method. Outcome of the numerical results reveals that the REAOR iterative method is more efficient when compared with Extended Accelerated Over-Relaxation iterative method in terms of computational time, level of accuracy and required number of iterations for convergence