A meshless based method for solution of integral equations
A meshless based method for solution of integral equations
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DOI：
10.1016/j.apnum.2009.12.003
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发表时间：
2010-03
影响因子：
2.8
通讯作者：
D. Mirzaei
中科院分区：
文献类型：
--
作者：
D. Mirzaei
本文提出了一种基于移动最小二乘法(MLS)求解一维和二维空间积分方程组的数值格式。对于最小二乘法，利用分布在分析域上的节点来近似未知的物理量。该方法是一种无网格方法，因为它不需要任何背景内插或近似单元，也不依赖于区域的几何形状。因此，对于二维Fredholm型积分方程解，可以考虑非矩形区域。给出了新方法的误差分析。该方案结构简单，具有较强的计算吸引力。通过实例说明了该方法的应用。
This article describes a numerical scheme based on the moving least squares (MLS) method for solving integral equations in one- and two-dimensional spaces. For the MLS, nodal points spread over the analyzed domain, are utilized to approximate the unknown physical quantities. The method is a meshless method, since it does not require any background interpolation or approximation cells and it dose not depend to the geometry of domain. Thus for the two-dimensional Fredholm integral equation, a non-rectangular domain can be considered. Error analysis is provided for the new method. The proposed scheme is simple and computationally attractive. Applications are demonstrated through illustrative examples.