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首页> 外文期刊>Advanced Science Letters >Half-Sweep AOR Iteration with Rotated Nonlocal Arithmetic Mean Scheme for the Solution of 2D Nonlinear Elliptic Problems
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Half-Sweep AOR Iteration with Rotated Nonlocal Arithmetic Mean Scheme for the Solution of 2D Nonlinear Elliptic Problems

机译：具有旋转非识别算术平均方案的半扫描AOR迭代，用于2D非线性椭圆问题解决方案

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摘要

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-pointrotated 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 thesystem 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 SuccessiveOver-relaxation (FSSOR) and Half-Sweep Successive Over Relaxation (HSSOR).
机译：在本文中，我们处理半扫描加速在弛豫（HSAOR）方法中的应用，以解决二维非线性椭圆边值问题的非识别离散化方案。 为此，我们提出了一种新的非局部算术平均方案，即在提议的问题中施加到任何非线性术语中的四分之一的非局部算术平均方案。 通过使用二阶有限差分方案，已经导出了半扫描非线性近似方程。 然后，应用非识别离散化方案以将非线性近似方程的关系转换为线性方程的相应系统。 在整个数值结果中，与迭代的数量，执行时间和最大误差相比，所提出的HSOOR方法与放松的全部扫描连续（FSSOR）和半扫描相比，所提出的HSAOR方法在迭代数量，执行时间和最大误差方面优越。

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