scholarly journals Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions

2006 ◽  
Vol 44 (11-12) ◽  
pp. 1160-1168 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mehdi Tatari
Keyword(s):  
Parabolic Equation ◽  
Radial Basis Functions ◽  
Control Parameter ◽  
Basis Functions ◽  
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.

scholarly journals Radial Basis Functions Intended to Determine the Upper Bound of Absolute Dynamic Error at the Output of Voltage-Mode Accelerometers

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4154 ◽  
Author(s):  
Krzysztof Tomczyk ◽  
Marcin Piekarczyk ◽  
Grzegorz Sokal
Keyword(s):  
Mathematical Model ◽  
Radial Basis Functions ◽  
Upper Bound ◽  
Dynamic Error ◽  
Basis Functions ◽  
Voltage Mode ◽  
Radial Basis ◽  
Operational Frequency ◽  
Mc Method

In this paper, we propose using the radial basis functions (RBF) to determine the upper bound of absolute dynamic error (UAE) at the output of a voltage-mode accelerometer. Such functions can be obtained as a result of approximating the error values determined for the assumed-in-advance parameter variability associated with the mathematical model of an accelerometer. This approximation was carried out using the radial basis function neural network (RBF-NN) procedure for a given number of the radial neurons. The Monte Carlo (MC) method was also applied to determine the related error when considering the uncertainties associated with the parameters of an accelerometer mathematical model. The upper bound of absolute dynamic error can be a quality ratio for comparing the errors produced by different types of voltage-mode accelerometers that have the same operational frequency bandwidth. Determination of the RBFs was performed by applying the Python-related scientific packages, while the calculations related both to the UAE and the MC method were carried out using the MathCad program. Application of the RBFs represent a new approach for determining the UAE. These functions allow for the easy and quick determination of the value of such errors.

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