High-order compact schemes for fractional differential equations with mixed derivatives

2017 ◽  
Vol 33 (6) ◽  
pp. 2141-2158
Author(s):  
Seakweng Vong ◽  
Chenyang Shi ◽  
Pin Lyu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
High Order ◽  
Compact Schemes ◽  
Mixed Derivatives ◽  
Fractional Differential

Convergence Analysis of a High Order Schema for the Ordinary Fractional Diffusion Equation

2014 ◽  
Vol 602-605 ◽  
pp. 3088-3091
Author(s):  
Jun Ying Cao ◽  
Zi Qiang Wang
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Convergence Analysis ◽  
Fractional Differential Equations ◽  
Fractional Diffusion ◽  
High Order ◽  
Fractional Diffusion Equation ◽  
Block Method ◽  
Fractional Differential ◽  
Block Approach

The block-by-block method extended by Kumar and Agrawal to fractional differential equations. Cao et al. proposed a high order schema which is based on an improved block-by-block approach, which consists in finding 4 unknowns simultaneously at each step block through solving a 4 × 4 system. We rigorously analytically prove that this method is convergent with order for , and order 6 for .

scholarly journals High order algorithms for numerical solution of fractional differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Shahbazi Asl ◽  
Mohammad Javidi ◽  
Yubin Yan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Algorithms ◽  
Interpolation Polynomial ◽  
High Order ◽  
The Novel ◽  
Fractional Differential ◽  
Novel Algorithms ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.

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