Error estimate for the numerical solution of fractional reaction-subdiffusion process based on a meshless method

چکیده مقاله

Inthispaperanumericaltechniquebasedonameshlessmethodisproposedforsolvingthe timefractionalreaction–subdiffusionequation.Firstly,weobtainatimediscretescheme basedonafinitedifferencescheme,thenweusethemeshlessGalerkinmethod,toapprox- imate the spatial derivatives and obtain a full discrete scheme. In the proposed scheme, some integrals appear over the boundary and the domain of problem which will be ap- proximatedusingGauss–Legendrequadraturerule.Then,weprovethatthetimediscrete schemeisunconditionallystableandconvergentusingtheenergymethod.Weshowcon- vergence order of the time discrete scheme is O (τγ ). The aim of this paper is to obtain an error estimate and to show convergence for the meshless Galerkin method based on theradialbasisfunctions.Numericalexamplesconfirmtheefficiencyandaccuracyofthe proposedscheme.