scholarly journals A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains

2015 ◽  
Vol 66 (1) ◽  
pp. 67-90 ◽  
Author(s):  
Yanlai Chen ◽  
Sigal Gottlieb ◽  
Alfa Heryudono ◽  
Akil Narayan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Irregular Domains ◽  
Partial Differential ◽  
Radial Basis ◽  
Radial Basis Function Method

scholarly journals A symmetric integrated radial basis function method for solving differential equations

2018 ◽  
Vol 34 (3) ◽  
pp. 959-981 ◽  
Author(s):  
Nam Mai-Duy ◽  
Deepak Dalal ◽  
Thi Thuy Van Le ◽  
Duc Ngo-Cong ◽  
Thanh Tran-Cong
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Radial Basis ◽  
Radial Basis Function Method

scholarly journals A Novel Meshfree Approach with a Radial Polynomial for Solving Nonhomogeneous Partial Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 270
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao ◽  
Chih-Yu Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Numerical Solutions ◽  
Polynomial Basis ◽  
Partial Differential ◽  
Minimum Order ◽  
Radial Basis

In this article, a novel radial–based meshfree approach for solving nonhomogeneous partial differential equations is proposed. Stemming from the radial basis function collocation method, the novel meshfree approach is formulated by incorporating the radial polynomial as the basis function. The solution of the nonhomogeneous partial differential equation is therefore approximated by the discretization of the governing equation using the radial polynomial basis function. To avoid the singularity, the minimum order of the radial polynomial basis function must be greater than two for the second order partial differential equations. Since the radial polynomial basis function is a non–singular series function, accurate numerical solutions may be obtained by increasing the terms of the radial polynomial. In addition, the shape parameter in the radial basis function collocation method is no longer required in the proposed method. Several numerical implementations, including homogeneous and nonhomogeneous Laplace and modified Helmholtz equations, are conducted. The results illustrate that the proposed approach may obtain highly accurate solutions with the use of higher order radial polynomial terms. Finally, compared with the radial basis function collocation method, the proposed approach may produce more accurate solutions than the other.

Sign in / Sign up

Export Citation Format

Share Document