scholarly journals Radial Basis Functions Based Differential Quadrature Method for One Dimensional Heat Equation

2021 ◽  
Vol 6 (2) ◽  
pp. 35
Author(s):  
Kedir Aliy ◽  
Alemayehu Shiferaw ◽  
Hailu Muleta
Keyword(s):  
Heat Equation ◽  
Radial Basis Functions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Basis Functions ◽  
Quadrature Method ◽  
One Dimensional ◽  
Radial Basis

scholarly journals Entropy stable essentially nonoscillatory methods based on RBF reconstruction

2019 ◽  
Vol 53 (3) ◽  
pp. 925-958 ◽  
Author(s):  
Jan S. Hesthaven ◽  
Fabian Mönkeberg
Keyword(s):  
Radial Basis Functions ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Basis Functions ◽  
One Dimensional ◽  
Hyperbolic Conservation ◽  
Radial Basis ◽  
Sign Property ◽  
Entropy Stable ◽  
Essentially Nonoscillatory

To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second order finite volume method (RBF-EFV2) for one-dimensional problems. Thus, we show that methods based on radial basis functions are as powerful as methods based on polynomial reconstruction. The main contribution is the construction of an algorithm and a smoothness indicator that ensures an interpolation function which fulfills the sign-property on general one dimensional grids.

Sign in / Sign up

Export Citation Format

Share Document