Trigonometric spectral collocation methods on lattices

2003 ◽  
pp. 121-132 ◽  
Author(s):  
Dong Li ◽  
Fred J. Hickernell
Keyword(s):  
Collocation Methods ◽  
Spectral Collocation ◽  
Spectral Collocation Methods

scholarly journals NEW RECURSIVE APPROXIMATIONS FOR VARIABLE-ORDER FRACTIONAL OPERATORS WITH APPLICATIONS

2018 ◽  
Vol 23 (2) ◽  
pp. 227-239 ◽  
Author(s):  
Mahmoud A. Zaky ◽  
Eid H. Doha ◽  
Taha M. Taha ◽  
Dumitru Baleanu
Keyword(s):  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Collocation Methods ◽  
Fractional Integrals ◽  
Variable Order ◽  
Spectral Collocation ◽  
Fractional Differential ◽  
Derivatives Of ◽  
Spectral Collocation Methods ◽  
Numerical Approaches

To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation.In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional initial value problems on the half line. Specifically, we derive three-term recurrence relations to efficiently calculate the variable-order fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.

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