A Direct Prediction of the Shape Parameter in the Collocation Method of Solving Poisson Equation

Lin-Tian Luh ()
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Lin-Tian Luh: Department of Data Science and Big Data Analytics, Providence University, Shalu, Taichung 43310, Taiwan

Mathematics, 2022, vol. 10, issue 19, 1-18

Abstract: In this paper, we totally discard the traditional trial-and-error algorithms of choosing the acceptable shape parameter c in the multiquadrics − c 2 + ∥ x ∥ 2 when dealing with differential equations, for example, the Poisson equation, with the RBF collocation method. Instead, we choose c directly by the MN-curve theory and hence avoid the time-consuming steps of solving a linear system required by each trial of the c value in the traditional methods. The quality of the c value thus obtained is supported by the newly born choice theory of the shape parameter. Experiments demonstrate that the approximation error of the approximate solution to the differential equation is very close to the best approximation error among all possible choices of c .

Keywords: radial basis function; multiquadric; shape parameter; collocation; Poisson equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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