Polynomial–Sinc collocation method combined with the Legendre–Gauss quadrature rule for numerical solution of distributed order fractional differential equations

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Nasrin Moshtaghi ◽  
Abbas Saadatmandi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
Fractional Differential ◽  
Gauss Quadrature Rule ◽  
Distributed Order

Numerical solution of fractional differential equations by using fractional B-spline

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Hossein Jafari ◽  
Chaudry Khalique ◽  
Mohammad Ramezani ◽  
Haleh Tajadodi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Spline Collocation ◽  
B Spline ◽  
Computational Work ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

AbstractIn this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.

SPECTRAL COLLOCATION METHOD FOR MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 11 (05) ◽  
pp. 1350072 ◽  
Author(s):  
F. GHOREISHI ◽  
P. MOKHTARY
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Jacobi Polynomials ◽  
Transformation Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Fractional Differential ◽  
New Equation

In this paper, the spectral collocation method is investigated for the numerical solution of multi-order Fractional Differential Equations (FDEs). We choose the orthogonal Jacobi polynomials and set of Jacobi Gauss–Lobatto quadrature points as basis functions and grid points respectively. This solution strategy is an application of the matrix-vector-product approach in spectral approximation of FDEs. The fractional derivatives are described in the Caputo type. Numerical solvability and an efficient convergence analysis of the method have also been discussed. Due to the fact that the solutions of fractional differential equations usually have a weak singularity at origin, we use a variable transformation method to change some classes of the original equation into a new equation with a unique smooth solution such that, the spectral collocation method can be applied conveniently. We prove that after this regularization technique, numerical solution of the new equation has exponential rate of convergence. Some standard examples are provided to confirm the reliability of the proposed method.

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