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Solving Poisson Equations by the MN-Curve Approach.

Authors :
Luh, Lin-Tian
Source :
Mathematics (2227-7390). Dec2022, Vol. 10 Issue 23, p4582. 11p.
Publication Year :
2022

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
22277390
Volume :
10
Issue :
23
Database :
Academic Search Index
Journal :
Mathematics (2227-7390)
Publication Type :
Academic Journal
Accession number :
160742296
Full Text :
https://doi.org/10.3390/math10234582