Spectral collocation method for nonlinear Riemann–Liouville fractional differential system

CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Zhendong Gu ◽  
Yinying Kong
Keyword(s):  
Collocation Method ◽  
Differential System ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Fractional Differential System ◽  
Fractional Differential

scholarly journals Applications of Legendre spectral collocation method for solving system of time delay differential equations

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402092211
Author(s):  
Sami Ullah Khan ◽  
Ishtiaq Ali
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Collocation Method ◽  
Differential System ◽  
Numerical Test ◽  
Spectral Collocation Method ◽  
Numerical Techniques ◽  
Spectral Collocation ◽  
Delay Differential System ◽  
Delay Differential

The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the approximate solution of time delay differential system. Legendre spectral collocation method and their properties are applied to determined the general procedure for solving time delay differential system with detail error and convergence analysis. The method first convert the proposed system to a system of ordinary differential equations and then apply the Legendre polynomials to solve the resultant system efficiently. Finally, some numerical test problems are given to confirm the efficiency of the method and were compared with other available numerical schemes in the literature.

scholarly journals A spectral collocation method for the coupled system of nonlinear fractional differential equations

2022 ◽  
Vol 7 (4) ◽  
pp. 5670-5689
Author(s):  
Xiaojun Zhou ◽  
◽  
Yue Dai
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Caputo Fractional Derivatives ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Given

<abstract><p>This paper analyzes the coupled system of nonlinear fractional differential equations involving the caputo fractional derivatives of order $ \alpha\in(1, 2) $ on the interval (0, T). Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations, then the resulting equation is discretized by using a spectral method based on the Legendre polynomials. We have constructed a Legendre spectral collocation method for the coupled system of nonlinear fractional differential equations. The error bounds under the $ L^2- $ and $ L^{\infty}- $norms is also provided, then the theoretical result is validated by a number of numerical tests.</p></abstract>

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