Approximate solution for 2 dimensional fuzzy parabolic equations in QSAGE iterative method

Dahalan, A. A.; Sulaiman, Jumat

doi:10.12988/ijma.2015.516

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…If the temperature values show no more changes, the loop will end and the variance of computation values should be diminutive, i.e. 15 1.0 − . This overhead precision is required in the solutions to avert the development of a flat area, better known as saddle points, from failing the generation of paths.…”

Section: Experiments and Resultsmentioning

confidence: 99%

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

2021

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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.

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Section: Experiments and Resultsmentioning

confidence: 99%

“…The results of this paper can essentially be categorized as a family of full-sweep iterations. In addition to the concept of full-sweep iteration, advance research on half-sweep [13,14] and quarter-sweep [15] iterations will improve the convergence rate of the suggested standard iterative methods.…”

Section: Discussionmentioning

confidence: 99%

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

2021

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“…The results of this paper can essentially be categorized as family of full-sweep iterations. In addition to the full-sweep iteration concept, further analysis on half-sweep [15,[18][19][20][21] and quarter-sweep [22][23][24][25] iterations can be also considered with a view to speeding up the convergence rate of the standard proposed iterative methods.…”

Section: Discussionmentioning

confidence: 99%

Path Finding of Static Indoor Mobile Robot via Aor Iterative Method Using Harmonic Potentials

Ahmad Dahalan,

Saudi,

Sulaiman

2020

ZJDSET

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Mobile robots often have to discover a path of collision-free towards a specific goal point in their environment. We are trying to resolve the mobile robot problem iteratively by means of numerical technique. It is built on a method of potential field that count on the use of Laplace’s equation in the mobile robot’s configuration space to constrain/which reduces the generation of a potential function over regions. This paper proposed an iterative approach in solving robot path finding problem known as Accelerated Over-Relaxation (AOR). The experiment shows that these suggested approach can establish a smooth pat between the starting and goal points by engaging with a finite-difference technique. The simulation results also show that a more rapidly solution with smoother path than the previous work is achieved via this numerical approach.

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“…Basically the results of this paper can be classified as one of half-sweep iteration. Apart from the concept of the half-sweep iteration, further investigation on quarter-sweep [19][20][21][22][22][23][24][25] iterations can also be considered in order to speed up the convergence rate of the standard proposed iterative methods. Other than that, further study will be extended to solve non-linear problem by combining Newton-Raphson method.…”

Section: Discussionmentioning

confidence: 99%

Half-sweep two parameter alternating group explicit iterative method applied to fuzzy Poisson equation

Dahalan¹,

Sulaiman²

2016

ams

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Iterative methods particularly the Two Parameter Alternating Group Explicit (TAGE) methods are used to solve system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs). The formulation and implementation of the Full-Sweep TAGE (FSTAGE) and Half-Sweep TAGE (HSTAGE) methods are also presented. Then numerical experiments are carried out onto two example problems to verify the effectiveness of the method. The results show that TAGE method is superior compare to AGE method in the aspect of number of iterations, execution time and Hausdorff distance.

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Approximate solution for 2 dimensional fuzzy parabolic equations in QSAGE iterative method

Cited by 10 publications

References 12 publications

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

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

Path Finding of Static Indoor Mobile Robot via Aor Iterative Method Using Harmonic Potentials

Half-sweep two parameter alternating group explicit iterative method applied to fuzzy Poisson equation

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