Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials

2013 ◽  
Vol 37 (3) ◽  
pp. 329-342 ◽  
Author(s):  
J.A. Rad ◽  
S. Kazem ◽  
M. Shaban ◽  
K. Parand ◽  
A. Yildirim
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Bernstein Polynomials ◽  
Tau Method ◽  
Fractional Differential

scholarly journals Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Qingxue Huang ◽  
Fuqiang Zhao ◽  
Jiaquan Xie ◽  
Lifeng Ma ◽  
Jianmei Wang ◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
Numerical Approach ◽  
Principal Characteristic ◽  
Legendre Functions ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Fractional Differential

In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.

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