High-Order Accurate Local Schemes for Fractional Differential Equations

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• 作者：Daniel Baffet ; Jan S. Hesthaven
• 关键词：Fractional differential equations ; Volterra equations ; High ; order methods
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：70
• 期：1
• 页码：355-385
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted \(L^2\) space. To obtain the schemes this expansion is terminated after \(P+1\) terms. We study the local truncation error and its behavior with respect to the step-size h and P. Building on this analysis, we develop an error indicator based on the Milne device. Methods with fixed and variable step-size are tested numerically on a number of problems, including problems with known solutions, and a fractional version on the Van der Pol equation.