Mathematics

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Mathematics

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

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    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
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    Numerical Solution of Parabolic Partial Differential Equations via Conjugate Gradient Technique
    (Nigeria Mathematical Science (NMS), 2023-06-19) Khadeejah James Audu
    Parabolic partial differential equations (PPDEs) arise in many areas of science and engineering, including heat transfer, diffusion, and fluid dynamics. Analytical solutions to these PPDEs are often difficult or impossible to obtain, so numerical methods are needed to approximate the solution. In this research, we investigate the use of the conjugate gradient technique for numerically solving parabolic PDEs. The technique involves discretizing the PPDE with regard to both space and time. The parabolic partial differential equations are then transformed into systems of linear algebraic equations using the Crank-Nicholson centred difference approach. Then, these equations are solved to yield the unknown points in the grids, which are subsequently substituted into the assumed solution to obtain the required estimated solution, which is reported in tabular format. A comparison was made between the conjugate gradient solutions and those produced using the Jacobi preconditioned conjugate gradient technique in terms of the time required and rate of convergence at that point. Results indicate that conjugate gradient techniques are suitable for solving parabolic-type partial differential equations, with Jacobi-preconditioned conjugate gradient technique converging faster. This research has potential applications in various areas of science and engineering where parabolic PDEs arise
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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.