scholarly journals Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problem

2020 ◽  
Vol 90 (327) ◽  
pp. 19-40
Author(s):  
Natalia Kopteva
Keyword(s):  
Error Analysis ◽  
Fractional Order ◽  
Parabolic Problem ◽  
Type Method ◽  
Graded Meshes

A Numerical Algorithm to Initial Value Problem of Caputo Fractional-Order Differential Equation

2015 ◽  
Author(s):  
Lu Bai ◽  
Dingyü Xue
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Fractional Order ◽  
Numerical Algorithm ◽  
Initial Value Problem ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Initial Value

A numerical algorithm is presented to solve the initial value problem of linear and nonlinear Caputo fractional-order differential equations. Firstly, nonzero initial value problem should be transformed into zero initial value problem. Error analysis has been done to polynomial algorithm, the reason has been found why the calculation error of the algorithm is large. A new algorithm called exponential function algorithm is proposed based on the analysis. The obtained fractional-order differential equation is transformed into difference equation. If the differential equation is linear, the obtained difference equation is explicit, the numerical solution can be solved directly; otherwise, the obtained difference equation is implicit, the predictor of the numerical solution can be obtained with extrapolation algorithm, substitute the predictor into the equation, the corrector can be solved. Error analysis has been done to the new algorithm, the algorithm is of first order.

Type Number Based Steady-State Error Analysis on Fractional Order Control Systems

2016 ◽  
Vol 19 (1) ◽  
pp. 266-278
Author(s):  
Jinwen Pan ◽  
Qing Gao ◽  
Jianbin Qiu ◽  
Yong Wang
Keyword(s):  
Steady State ◽  
Error Analysis ◽  
Control Systems ◽  
Fractional Order ◽  
Type Number ◽  
Fractional Order Control ◽  
State Error
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