A review of radial basis function with applications explored
Arora, G., Bala, K., Emadifar, H., Khademi, M. (2023). A review of radial basis function with applications explored. EKB Journal Management System, 31(1), 1-14. doi: 10.1186/s42787-023-00164-3
Geeta Arora; Kiran Bala; Homan Emadifar; Masoumeh Khademi. "A review of radial basis function with applications explored". EKB Journal Management System, 31, 1, 2023, 1-14. doi: 10.1186/s42787-023-00164-3
Arora, G., Bala, K., Emadifar, H., Khademi, M. (2023). 'A review of radial basis function with applications explored', EKB Journal Management System, 31(1), pp. 1-14. doi: 10.1186/s42787-023-00164-3
Arora, G., Bala, K., Emadifar, H., Khademi, M. A review of radial basis function with applications explored. EKB Journal Management System, 2023; 31(1): 1-14. doi: 10.1186/s42787-023-00164-3

A review of radial basis function with applications explored

Journal of the Egyptian Mathematical Society
Volume 31, Issue 1, 2023, Page 1-14  XML PDF (1.47 MB)
Document Type: Original Article
DOI: 10.1186/s42787-023-00164-3
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Authors
Geeta Arora1; Kiran Bala1; Homan Emadifar2; Masoumeh Khademi2
1Department of Mathematics, Lovely Professional University, Punjab, India
2Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
Abstract
Partial differential equations are a vital component of the study of mathematical
models in science and engineering. There are various tools and techniques developed
by the researchers to solve the differential equations. The radial basis functions have
proven to be an efficient basis function for approximating the solutions to ordinary
and partial differential equations. There are different types of radial basis function
methods that have been developed by the researchers to solve various well known
differential equation. It has been developed for approximation of the solution with various
approaches that lead to the development of hybrid methods. Radial basis function
methods are widely used in numerical analysis and statistics because of their
ability to deal with meshless domain. In this work, the different radial basis function
approaches were investigated along with the focus on the strategies being addressed
to find the shape parameter value. The mathematical formulations of the various radial
basis function methods are discussed along with the available shape parameters to get
the optimal value of the numerical solutions. The present work will lay a foundation
to understand the development of the radial basis functions that could lead to a play
an important role in development of method thereafter.
Keywords
Partition of unity; Shape parameter; Partial differential equation; Kansa collocation method; Radial basis function
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