New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation | Zendy

Peixian Zhuang | Zendy; F. Liu | Zendy; Vo Anh | Zendy; Ian Turner | Zendy

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New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation

Author(s) -

Peixian Zhuang,

F. Liu,

Vo Anh,

Ian Turner

Publication year - 2008

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/060673114

Subject(s) - mathematics , convergence (economics) , numerical analysis , stability (learning theory) , anomalous diffusion , diffusion equation , fractional calculus , differential equation , order of accuracy , numerical stability , energy method , mathematical analysis , computer science , knowledge management , innovation diffusion , economy , service (business) , machine learning , economics , economic growth

A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.

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