A time–efficient variable shape parameter Kansa–radial basis function method for the solution of nonlinear boundary value problems

2022 ◽  
Vol 413 ◽  
pp. 126613
Author(s):  
Andreas Karageorghis
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Function Method ◽  
Shape Parameter ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Variable Shape ◽  
Radial Basis Function Method

scholarly journals The Conical Radial Basis Function for Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
J. Zhang ◽  
F. Z. Wang ◽  
E. R. Hou
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Computational Cost ◽  
Basis Functions ◽  
Simple Scheme ◽  
Collocation Points ◽  
Radial Basis ◽  
Radial Basis Function Method

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

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