A meshless based method for solution of integral equations

作者：Mirzaei Davoud; Dehghan Mehdi^*

来源：Applied Numerical Mathematics, 2010, 60(3): 245-262.

DOI：10.1016/j.apnum.2009.12.003

• Fredholm integral equation
• Volterra integral equation
• Moving least squares (MLS) approximation
• Error analysis

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.

• 出版日期2010-3