Articles you may be interested inNumerical solutions for linear Fredholm integral equations of the second kind using 2-point half-sweep explicit group method AIP Conf. ABCs and fourth-order spline collocation for the solution of two-point boundary value problems over an infinite domain AIP Conf. Proc. 1558, 372 (2013); 10.1063/1.4825501 Quarter-sweep Gauss-Seidel method with quadratic spline scheme applied to fourth order two-point boundary value problems AIP Conf. Proc. 1522, 735 (2013); 10.1063/1.4801199Successive over relaxation method in solving two-point fuzzy boundary value problems AIP Conf.Abstract. The main purpose of this paper is to examine the application of complexity reduction approach based on halfsweep iteration concept with Alternating Group Explicit (AGE) method namely Half-Sweep AGE (HSAGE) method for solving system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs). To form the linear system, the corresponding second order finite difference scheme has been used to derive the half-sweep finite difference approximation equation of the problems. The formulation and implementation of the proposed iterative method are discussed. Furthermore, numerical results of two test problems are also included in order to verify performance of the method compared to Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep AGE (FSAGE) methods. The findings show that the proposed HSAGE method is superior to other tested methods in the sense of number of iterations, execution time and Hausdorff distance.

One of the main issues when dealing with mobile robot navigation is that we have to resolve the obstacle avoidance problem, where when moving from a starting point to the goal point, the mobile robot will have to generate a collision-free path in order ensure that it can move efficiently in the environment. In this study, we attempt to resolve the issue by solving it iteratively via numerical technique. This solution is based on the potential field method that utilizes the Laplace’s equation to constrain the generation of potential functions over the regions in the configuration space where the mobile robot operates in. This paper proposed Modified Accelerated Over-Relaxation (MAOR) iterative method for solving robot path planning problem. Through the application of finite-difference technique in it, the experiment shows that the mobile robot is able to generate a smooth path from starting point to goal point. Furthermore, the results obtained from the simulation has shown that this numerical method was able to perform faster solution and generated smoother path comparing the previous works on the similar problem.

No abstract

In this study, numerical methods are considered in solving the fuzzy boundary value problem (FBVP). This boundary value problem will then be discretized to derive second order finite difference equation and hence generated fuzzy linear system. The approximation solver towards system of linear equations is described through the implementation of the Gauss-Seidel (GS) and Successive Over Relaxation (SOR) iterative methods. Then several numerical experiments were shown to illustrate the effectiveness of SOR iterative method compared with the GS method.

In this study, iterative methods particularly families of Alternating Group Explicit (AGE) methods are used to solve system of linear equations generated from the discretization of two-dimensional fuzzy diffusion problems. The formulation and implementation of the Full-Sweep AGE (FSAGE), Half-Sweep AGE (HSAGE) and Quarter-Sweep AGE (QSAGE) methods were also presented. Then numerical experiments are carried out onto two example problems to verify the effectiveness of the methods.