Nonlinear fractional integro-differential reaction-diffusion equation via radial basis functions

2015 ◽  
Vol 130 (3) ◽  
Author(s):  
Mohammad Aslefallah ◽  
Elyas Shivanian
Keyword(s):  
Diffusion Equation ◽  
Radial Basis Functions ◽  
Reaction Diffusion ◽  
Basis Functions ◽  
Reaction Diffusion Equation ◽  
Differential Reaction ◽  
Radial Basis

scholarly journals Numerical investigation of the two– dimensional time–dependent diffusion equation using Radial basis functions

2020 ◽  
Vol 22 (2) ◽  
pp. 293-304
Author(s):  
Hamid Mesgarani ◽  
◽  
Masoud Bakhshandeh ◽  
Yones Esmaeelzade Aghdam ◽  
◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Numerical Investigation ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Time Dependent ◽  
Two Dimensional ◽  
Radial Basis

Time fractional modified anomalous sub-diffusion equation with a nonlinear source term through locally applied meshless radial point interpolation

2018 ◽  
Vol 32 (22) ◽  
pp. 1850251 ◽  
Author(s):  
Elyas Shivanian ◽  
Ahmad Jafarabadi
Keyword(s):  
Diffusion Equation ◽  
Radial Basis Functions ◽  
Source Term ◽  
Interpolation Method ◽  
Two Dimensions ◽  
Basis Functions ◽  
Nonlinear Source ◽  
Radial Point Interpolation ◽  
Radial Basis ◽  
Point Interpolation

In this paper, an alternative approach of spectral meshless radial point interpolation (SMRPI) is applied to the modified anomalous fractional sub-diffusion equation with a nonlinear source term in one and two dimensions. The time fractional derivative is described in the Riemann–Liouville sense. The applied approach is based on a combination of meshless methods and the spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct the shape functions which act as basis functions in the frame of the SMRPI. It is proved that the scheme is unconditionally stable with respect to the time variable in [Formula: see text] and convergent with the order of convergence [Formula: see text], [Formula: see text]. In this work, the thin plate splines (TPS) are used as the radial basis functions. In order to eliminate the nonlinearity, a simple predictor–corrector (P–C) scheme is used. The results of numerical experiments are compared to the analytical solutions in order to confirm the accuracy and the efficiency of the presented scheme.

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