Performance Analysis of Half-Sweep Successive Over-Relaxation Iterative Method for Solving Four-Point Composite Closed Newton-Cotes System

2016 ◽  
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Thaw Zin Htun ◽  
Elayaraja Aruchunan ◽  
Majid Khan Majahar Ali ◽  
Jumat Sulaiman
Keyword(s):  
Performance Analysis ◽  
Iterative Method ◽  
Successive Over Relaxation

scholarly journals Solutions of reaction-diffusion equations using similarity reduction and HSSOR iteration

2019 ◽  
Vol 16 (3) ◽  
pp. 1430
Author(s):  
Nur Afza Mat Ali ◽  
Rostang Rahman ◽  
Jumat Sulaiman ◽  
Khadizah Ghazali
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Iterative Method ◽  
Iterative Methods ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Sparse Linear System ◽  
Successive Over Relaxation ◽  
Number Of Iterations

<p>Similarity method is used in finding the solutions of partial differential equation (PDE) in reduction to the corresponding ordinary differential equation (ODE) which are not easily integrable in terms of elementary or tabulated functions. Then, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is applied in solving the sparse linear system which is generated from the discretization process of the corresponding second order ODEs with Dirichlet boundary conditions. Basically, this ODEs has been constructed from one-dimensional reaction-diffusion equations by using wave variable transformation. Having a large-scale and sparse linear system, we conduct the performances analysis of three iterative methods such as Full-sweep Gauss-Seidel (FSGS), Full-sweep Successive Over-Relaxation (FSSOR) and HSSOR iterative methods to examine the effectiveness of their computational cost. Therefore, four examples of these problems were tested to observe the performance of the proposed iterative methods.  Throughout implementation of numerical experiments, three parameters have been considered which are number of iterations, execution time and maximum absolute error. According to the numerical results, the HSSOR method is the most efficient iterative method in solving the proposed problem with the least number of iterations and execution time followed by FSSOR and FSGS iterative methods.</p>

scholarly journals Solving second kind linear Fredholm integral equations via Quarter-Sweep SOR iterative method

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Jumat Sulaiman
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Integral Equations ◽  
Numerical Solutions ◽  
Fredholm Integral Equations ◽  
Quadrature Method ◽  
Numerical Tests ◽  
Successive Over Relaxation

In this paper, we consider the numerical solutions of linear Fredholm integral equations of the second kind. The Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method is applied to solve linear systems generated from discretization of the second kind linear Fredholm integral equations using quadrature method. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical tests and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method.

scholarly journals Using free softwear for solving one problem of mathematical physics

2020 ◽  
Vol 2020 (1) ◽  
pp. 84-93
Author(s):  
Aleksandra Martianova
Keyword(s):  
Difference Equation ◽  
Iterative Method ◽  
Programming Language ◽  
Mathematical Physics ◽  
General Purpose ◽  
Free Software ◽  
Two Dimensional ◽  
Dirichlet Conditions ◽  
Dimensional Array ◽  
Successive Over Relaxation

The article presents the solution of Laplace equation with Dirichlet conditions using free software: computer mathematics systems Maxima, Scilab, GNU Octave and general-purpose programming language Python. The algorithm for solving Laplace difference equation with Dirichlet conditions is realized by using the iterative method of successive over-relaxation and helps to obtain the solution in the form of a two-dimensional array of values and 3D-graphs. The resulting solution in the form of a two-dimensional array is compared with the test values. The resulting array was found to match the test values. The choice of a free software depends on the type of task and on personal preferences.

scholarly journals Robot pathfinding with obstacle avoidance capabilities in a static indoor environment via TOR iterative method using harmonic potentials

2021 ◽  
Vol 36 ◽  
pp. 04006
Author(s):  
A’Qilah Ahmad Dahalan ◽  
Azali Saudi ◽  
Jumat Sulaiman
Keyword(s):  
Iterative Method ◽  
Potential Field ◽  
Numerical Technique ◽  
Numerical Approach ◽  
Target Point ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Smooth Path ◽  
Successive Over Relaxation ◽  
Two Parameter

Mobile robots are always in a state where they have to find a collision-free path in their environment from start to the target point. This study tries to solve the problem of mobile robot iteratively by using a numerical technique. It is based on potential field technique that was modelled using the Laplace’s equation to restrain the creation of a potential functions across regions in the mobile robot’s configuration space. The gradient formed by the potential field is then used to generate a path for the robot to advance through. The present paper proposes a Two-Parameter Over-Relaxation (TOR) iterative method that is used to solve Laplace’s equation for obtaining the potential field that is then utilized for finding path of the robot, thus solving the robot pathfinding problem. The experiment indicates that it is capable of producing a smooth path between the starting and target points through the use of a finite-difference technique. Furthermore, the simulation results show that this numerical approach executes quicker and provides a smoother trail than to the previous works, that includes Successive Over-Relaxation (SOR) and Accelerated Over-Relaxation (AOR) methods.

scholarly journals Performance analysis of wireless networks based on time-scale separation: A new iterative method

2016 ◽  
Vol 86 ◽  
pp. 40-48 ◽  
Author(s):  
Luis Tello-Oquendo ◽  
Vicent Pla ◽  
Jorge Martinez-Bauset ◽  
Vicente Casares-Giner
Keyword(s):  
Wireless Networks ◽  
Performance Analysis ◽  
Iterative Method ◽  
Time Scale ◽  
Scale Separation ◽  
Time Scale Separation ◽  
New Iterative Method
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