On the effects of the radial basis function scale parameter on the numerical solution of partial differential equations

Hutchcraft, W. Elliott; Gordon, Richard K.
June 2009
Microwave & Optical Technology Letters;Jun2009, Vol. 51 Issue 6, p1520
Academic Journal
Radial Basis Functions have received significant attention in the scientific literature over the past several years. Specifically, they have been investigated extensively in the field of neural networks. They have been shown to have very good interpolation qualities and this property has led to the research presented in this letter. In this letter, radial basis functions are used in a meshless method using collocation to solve a simple electromagnetics problem; the main intent of this letter is to investigate the effects of the variation of the scale parameter present in the radial basis function. In particular, we will see its effects upon both the condition number of the resulting matrix and the solution accuracy. Some of the advantages and disadvantages of the proposed method will be discussed. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1520–1524, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24347


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