scholarly journals Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions

2009 ◽  
Vol 230 (2) ◽  
pp. 400-410 ◽  
Author(s):  
Mehdi Dehghan ◽  
Ali Shokri
Keyword(s):  
Numerical Solution ◽  
Radial Basis Functions ◽  
Gordon Equation ◽  
Basis Functions ◽  
Radial Basis ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040039 ◽  
Author(s):  
TAYYABA AKRAM ◽  
MUHAMMAD ABBAS ◽  
MUHAMMAD BILAL RIAZ ◽  
AHMAD IZANI ISMAIL ◽  
NORHASHIDAH MOHD. ALI
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Gordon Equation ◽  
Basis Functions ◽  
Unconditionally Stable ◽  
B Spline ◽  
Numerical Examples ◽  
Caputo’S Fractional Derivative ◽  
Klein Gordon ◽  
Klein Gordon Equation

A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo’s fractional derivative and the new approximation of ECBS together with [Formula: see text]-weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature.

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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