Radial basis function Hermite collocation approach for the solution of time dependent convection–diffusion problems

2005 ◽  
Vol 29 (4) ◽  
pp. 359-370 ◽  
Author(s):  
A. La Rocca ◽  
A. Hernandez Rosales ◽  
H. Power
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Time Dependent ◽  
Convection Diffusion ◽  
Radial Basis ◽  
Collocation Approach ◽  
Diffusion Problems

Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 69-76
Author(s):  
Fuzhang Wang ◽  
Kehong Zheng ◽  
Imtiaz Ahmad ◽  
Hijaz Ahmad
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Meshless Method ◽  
Absolute Error ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Radial Basis ◽  
Linear And Nonlinear ◽  
Physical Phenomena ◽  
Diffusion Problems

Abstract In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.

Sign in / Sign up

Export Citation Format

Share Document