A Fast High-Order Predictor–Corrector Method on Graded Meshes for Solving Fractional Differential Equations

Autor:	Xinxin Su, Yongtao Zhou
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	high-order predictor–corrector method graded meshes fractional differential equations sum-of-exponentials approximation error analysis Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 6, Iss 9, p 516 (2022)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract6090516
Popis:	In this paper, we focus on the computation of Caputo-type fractional differential equations. A high-order predictor–corrector method is derived by applying the quadratic interpolation polynomial approximation for the integral function. In order to deal with the weak singularity of the solution near the initial time of the fractional differential equations caused by the fractional derivative, graded meshes were used for time discretization. The error analysis of the predictor–corrector method is carefully investigated under suitable conditions on the data. Moreover, an efficient sum-of-exponentials (SOE) approximation to the kernel function was designed to reduce the computational cost. Lastly, several numerical examples are presented to support our theoretical analysis.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/edc2abd3860c4ec7b015c98d3082ae79 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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