Solving Poisson Equations by the MN-Curve Approach

Lin-Tian Luh ()
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Lin-Tian Luh: Department of Data Science, Providence University, Shalu, Taichung 43301, Taiwan

Mathematics, 2022, vol. 10, issue 23, 1-11

Abstract: In this paper, we adopt the choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Luh’s choice theory, based on harmonic analysis, is mathematically complicated and applies only to function interpolation. Here, we aim at presenting an easily accessible approach to solving differential equations with the choice theory which proves to be very successful, not only by its easy accessibility but also by its striking accuracy and efficiency. Our emphases are on the highly reliable prediction of the optimal value of the shape parameter and the extremely small approximation errors of the numerical solutions to the differential equations. We hope that our approach can be accepted by both mathematicians and non-mathematicians.

Keywords: radial basis functions; multiquadrics; shape parameter; collocation; Poisson equation; meshless method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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