Compactly supported kernels method of approximate particular solutions for solving elliptic problems

4th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Uddin, Marjan^1 ; Shed, Gul^1 ; Kamran^1 ; Ali, Amjad^1

Department of Basic Sciences and Islamiat, University of Engineering and Technology, Peshawar, Pakistan^1

关键词: Bench-mark problems;    Compactly supported;    Differentiation matrices;    Elliptic problem;    Engineering science;    Ill-conditioned;    Numerical scheme;    Particular solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012050/pdf
DOI  :  10.1088/1742-6596/633/1/012050

来源: IOP

【 摘 要 】

In this work the method of approximate particular solutions using compactly supported kernels is investigated. In the work of [1] the globally supported radial kernels for the construction of solution are used, and it is observed that for large scaled PDEs the differentiation matrix is ill-conditioned. We extended the work of [1] for compactly supported kernels, in order to solve large-scaled PDEs engineering sciences. The numerical scheme of the present method of approximate particular solutions is very accurate and simple in implementation. Three benchmark problems are solved by the present numerical scheme and the results are compared to other methods in the literature.