Stability and Convergence Analysis of a Class of Continuous Piecewise Polynomial Approximations for Time-Fractional Differential Equations

Zhou Han; Zegeling Paul Andries

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Stability and Convergence Analysis of a Class of Continuous Piecewise Polynomial Approximations for Time-Fractional Differential Equations

机译：一类时间分数阶微分方程的连续分段多项式逼近的稳定性和收敛性分析

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摘要

We propose and study a class of numerical schemes to approximate time-fractional differential equations. The methods are based on the approximations of the Caputo fractional derivative of order (0,1) by using continuous piecewise polynomials, which are strongly related to the backward differentiation formulae. We investigate their theoretical properties, such as the local truncation error and global error estimates with respect to sufficiently smooth solutions, and the numerical stability in terms of stability region and A(2)-stability. Numerical experiments are given to verify our theoretical investigations.

机译：我们提出并研究了一类近似时间分数阶微分方程的数值方案。该方法基于使用连续分段多项式的阶数（0,1）的Caputo分数导数的逼近，这与后向微分公式密切相关。我们研究它们的理论特性，例如关于足够光滑的解的局部截断误差和全局误差估计，以及根据稳定区域和A（2）-稳定性的数值稳定性。数值实验证明了我们的理论研究。

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来源
《Journal of Scientific Computing》 |2018年第1期|225-262|共38页
作者
Zhou Han; Zegeling Paul Andries;
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作者单位

Univ Utrecht, Dept Math, Utrecht, Netherlands;

Univ Utrecht, Dept Math, Utrecht, Netherlands;

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正文语种 eng
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关键词
Caputo fractional derivative; Continuous piecewise polynomial; Time-fractional differential equations; Stability; Convergence analysis;

机译：Caputo分数阶导数连续分段多项式时间分数阶微分方程稳定性收敛性分析;

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Stability and Convergence Analysis of a Class of Continuous Piecewise Polynomial Approximations for Time-Fractional Differential Equations

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