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A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

机译：分数阶微分方程数值解的预测 - 校正方法

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摘要

We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

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作者
Diethelm, Kai; Ford, Neville J.; Freed, Alan D.;
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年度 2002
页码 1-23
总页数 23
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
DIFFERENTIAL EQUATIONS; PREDICTOR-CORRECTOR METHODS; NUMERICAL ANALYSIS; NONLINEARITY; OPERATORS (MATHEMATICS); CONVOLUTION INTEGRALS; ALGORITHMS;

机译：微分方程;预测 - 修正方法;数值分析;非线性;经营者（数学）;卷积积分;算法;

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专利

1. A predictor-corrector approach for the numerical solution of fractional differential equations [J] . Diethelm K., Ford NJ., Freed AD. Nonlinear dynamics . 2002,第1a4期

机译：分数阶微分方程数值解的预测校正方法
2. A Newton interpolation based predictor-corrector numerical method for fractional differential equations with an activator-inhibitor case study [J] . Redouane Douaifia, Samir Bendoukha, Salem Abdelmalek Mathematics and computers in simulation . 2021,第Sepa期

机译：基于牛顿插值的基于预测测量校正器数值方法，其具有活化剂抑制作用案例研究的分数微分方程
3. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
4. A new predictor-corrector method for the numerical solution of fractional differential equations [C] . Jimin Yu, Chen Wang, Weihong Wu, International Conference on Machinery, Materials and Information Technology Applications . 2015

机译：用于分数微分方程数值解的新预测校正器方法
5. The numerical solutions of fractional differential equations with fractional Taylor vector [D] . Krishnasamy Saraswathy, Vidhya. 2016

机译：分数阶泰勒向量的分数阶微分方程的数值解
6. Data for numerical solution of Caputos and Riemann–Liouvilles fractional differential equations [O] . David E. Betancur-Herrera, Nicolas Muñoz-Galeano 2020

机译：Caputo和Riemann-Liouville分数阶微分方程数值解的数据
7. A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method [O] . Momenzadeh, Alireza, Ahrabi, Sima Sarv 2017

机译：分数阶微分数值解的比较方程：adams型预测校正器和多步广义差分变换方法

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

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