scholarly journals Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Maryam Sarboland ◽  
Azim Aminataei
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Radial Basis Functions ◽  
Taylor Series Expansion ◽  
Time Discretization ◽  
Basis Functions ◽  
One Dimensional ◽  
Radial Basis ◽  
The One ◽  
Rms Errors

During the last two decades, there has been a considerable interest in developing efficient radial basis functions (RBFs) algorithms for solving partial differential equations (PDEs). In this paper, we introduce the Petrov-Galerkin method for the numerical solution of the one-dimensional nonlinear Burger equation. In this method, the trial space is generated by the multiquadric (MQ) RBF and the test space is generated by the compactly supported RBF. In the time discretization of the equation, the Taylor series expansion is used. This method is applied on some test experiments, and the numerical results have been compared with the exact solutions. The , , and root-mean-square (RMS) errors in the solutions show the efficiency and the accuracy of the method.

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.

Numerical Solution of Foodstuff Freezing Problems Using Radial Basis Functions

2013 ◽  
Vol 19 (3) ◽  
pp. 1044-1047
Author(s):  
Antonino La Rocca ◽  
Vincenzo La Rocca ◽  
Antonio Messineo ◽  
Massimo Morale ◽  
Domenico Panno ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis
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