scholarly journals Solving space-fractional Cauchy problem by modified finite-difference discretization scheme

2020 ◽  
Vol 59 (4) ◽  
pp. 2409-2417 ◽  
Author(s):  
Omar Abu Arqub ◽  
Reem Edwan ◽  
Mohammed Al-Smadi ◽  
Shaher Momani
Keyword(s):  
Cauchy Problem ◽  
Finite Difference ◽  
Discretization Scheme ◽  
Finite Difference Discretization ◽  
Fractional Cauchy Problem ◽  
Difference Discretization

LEARNING IN RECURRENT FINITE DIFFERENCE NETWORKS

1995 ◽  
Vol 06 (03) ◽  
pp. 249-256 ◽  
Author(s):  
FU-SHENG TSUNG ◽  
GARRISON W. COTTRELL
Keyword(s):  
Finite Difference ◽  
Time Delays ◽  
Learning Algorithm ◽  
Time Constants ◽  
Learning Time ◽  
Discrete Algorithms ◽  
Finite Difference Discretization ◽  
Difference Discretization ◽  
Discrete Networks ◽  
Period Of Oscillation

A recurrent learning algorithm based on a finite difference discretization of continuous equations for neural networks is derived. This algorithm has the simplicity of discrete algorithms while retaining some essential characteristics of the continuous equations. In discrete networks learning smooth oscillations is difficult if the period of oscillation is too large. The network either grossly distorts the waveforms or is unable to learn at all. We show how the finite difference formulation can explain and overcome this problem. Formulas for learning time constants and time delays in this framework are also presented.

Sign in / Sign up

Export Citation Format

Share Document