scholarly journals Spline collocation methods for linear multi-term fractional differential equations

2011 ◽  
Vol 236 (2) ◽  
pp. 167-176 ◽  
Author(s):  
Arvet Pedas ◽  
Enn Tamme
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Fractional Differential

scholarly journals Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 185
Author(s):  
Angelamaria Cardone ◽  
Dajana Conte ◽  
Raffaele D’Ambrosio ◽  
Beatrice Paternoster
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Experiments ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Fractional Differential ◽  
Convergence And Stability Analysis

The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ordinary differential equations, and on two-step spline collocation methods for fractional differential equations. The construction of the methods together with the convergence and stability analysis are reported and some numerical experiments are carried out to show the efficiency of the proposed methods.

scholarly journals A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
D. Baleanu ◽  
A. H. Bhrawy ◽  
T. M. Taha
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Laguerre Polynomials ◽  
Collocation Methods ◽  
Half Line ◽  
Caputo Fractional Derivatives ◽  
Polynomial Degree ◽  
Generalized Laguerre Polynomials ◽  
Fractional Differential

This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomialsLi(α,β)(x)withx∈Λ=(0,∞),α>−1, andβ>0, andiis the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.

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