School of Physical Sciences (SPS)

Permanent URI for this communityhttp://197.211.34.35:4000/handle/123456789/48

School of Physical Sciences (SPS)

Browse

Subject: search.filters.subject.Convergence

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Computational Algorithm for Volterra Integral Solutions via Variational. Iterative Method
    (Paper Presentation at University of Lagos, Nigeria, 2023-08-28) Khadeejah James Audu
    The Volterra Integral Equations (VIE) are a class of mathematical equations that find applications in various fields, including physics, engineering, and biology. Solving VIEs analytically is often challenging, and researchers have turned to numerical methods for obtaining approximate solutions. In this research, we propose a computational algorithm based on the Variational Iterative Method (VIM) to efficiently and accurately solve VIEs. By incorporating this method into the computational algorithm, we aim to improve the accuracy and convergence rate of the solutions. The performance of our algorithm was evaluated through extensive numerical experiments on various types of VIEs. The results demonstrate the effectiveness of the VIM approach in terms of accuracy, convergence rate, and computational efficiency. In conclusion, the proposed computational algorithm based on VIM presents a valuable contribution to the field of solving VIEs. It offers an efficient and accurate approach for obtaining approximate solutions, enabling researchers and practitioners to tackle complex problems that rely on VIEs. The algorithm's versatility and robustness make it a promising tool for a wide range of applications, including physics, engineering, and biology.
  • No Thumbnail Available
    Item
    REFINEMENT OF PRECONDITIONED OVERRELAXATION ALGORITHM FOR SOLUTION OF THE LINEAR ALGEBRAIC SYSTEM 𝑨𝒙=𝒃
    (Faculty of Science, Kaduna State University, 2021) Ramatu Abdullahi; Raihanatu Muhammad
    In this paper, a refinement of preconditioned successive overrelaxation method for solving the linear system 𝐵𝑥=𝑐 is considered. The coefficient matrix 𝐵∈𝑅𝑛,𝑛 is a nonsingular real matrix, 𝑐∈𝑅𝑛 and 𝑥 is the vector of unknowns. Based on the usual splitting of the coefficient matrix 𝐵 as 𝐵=𝐷−𝐿𝐵−𝑈𝐵, the linear system is expressed as 𝐴𝑥=𝑏 or (𝐼−𝐿−𝑈)𝑥=𝑏; where 𝐿=𝐷−1𝐿𝐵, 𝑈=𝐷−1𝑈𝐵 and 𝑏=𝐷−1𝑐. This system is further preconditioned with a preconditioner of the type 𝑃=𝐼+𝑆 as 𝐴̅𝑥=𝑏̅ or (𝐷̅−𝐿̅−𝑈̅)𝑥=𝑏̅. A refinement of the resulting preconditioned successive overrelaxation (SOR) method is performed. Convergence of the resulting refinement of preconditioned SOR iteration is established and numerical experiments undertaken to demonstrate the effectiveness and efficiency of the method. Results comparison revealed that the refinement of SOR method converges faster than the preconditioned as well as the classical SOR method
  • No Thumbnail Available
    Item
    THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM
    (Federal University Dutsin MA Journal of Sciences (FJS), 2020-06) Muhammad R
    In this paper, we examine in details how to obtain the order, error constant, consistency and convergence of a Runge-Kutta Type method (RKTM) when the step number 𝑘 = 2. Analysis of the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. Due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation.