Half-Sweep AOR Iteration With Rotated Nonlocal Arithmetic Mean Scheme For The Solution Of 2D Nonlinear Elliptic Problems

Usran Alibudin, Mohd and Sunarto, Andang and Sulaiman, J and Saudi, A (2018) Half-Sweep AOR Iteration With Rotated Nonlocal Arithmetic Mean Scheme For The Solution Of 2D Nonlinear Elliptic Problems. American Saintific Publications, 3 (24). pp. 1922-1926. ISSN 1936-7317

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Abstract

In this paper, we deal with the application of Half-Sweep Accelerated Over Relaxation (HSAOR) method with nonlocal discretization scheme for solving two-dimensional nonlinear elliptic boundary value problems. To do this, we propose a new nonlocal arithmetic mean scheme namely the four-point rotated nonlocal arithmetic mean scheme being imposed into any nonlinear term in the proposed problems. By using the second order finite difference scheme, the half-sweep nonlinear approximation equation has been derived. Then, the nonlocal discretization scheme is applied to transform the system of nonlinear approximation equations into the corresponding system of linear equations. Throughout numerical results, it can be pointed out that the proposed HSAOR method was superior in terms of number of iterations, execution time and maximum error compared to Full-Sweep Successive Over-relaxation (FSSOR) and Half-Sweep Successive Over Relaxation (HSSOR).

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