On the convergence of piecewise polynomial collocation methods for variable-order space-fractional diffusion equations

Wenping Yuan, Hui Liang and Yanping Chen

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 209, issue C, 102-117

Abstract: In this study, we present a piecewise polynomial collocation method for the boundary-value problem of variable-order linear space-fractional diffusion equations. The proposed model is transformed to a weakly singular Volterra integral equation (VIE) of the second kind by an auxiliary variable, then a collocation method is constructed and analyzed for the obtained VIE. We demonstrate the existence and uniqueness of the collocation solution, as well as the optimal convergence order of the collocation method. Some numerical experiments are given to illustrate the theoretical results.

Keywords: Variable-order space-fractional diffusion equation; Volterra integral equation; Collocation method; Error analysis (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:209:y:2023:i:c:p:102-117

DOI: 10.1016/j.matcom.2023.02.013

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