Anzeige
Erschienen in:
2012 | OriginalPaper | Buchkapitel
A Compact Difference Scheme for Time Fractional Diffusion Equation with Neumann Boundary Conditions
verfasst von : Jianfei Huang, Yifa Tang, Wenjia Wang, Jiye Yang
Erschienen in: AsiaSim 2012
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
This paper is devoted to the numerical treatment of time fractional diffusion equation with Neumann boundary conditions. A compact difference scheme is derived for solving this problem, by combining the classic finite difference method for Caputo derivative in time, the second order central difference method in space and the compact difference treatment for Neumann boundary conditions. The solvability, stability and convergence of this scheme are rigorously discussed. We prove that the convergence order of this proposed scheme is
O
(
τ
2 −
α
+
h
2
), where
τ
,
α
and
h
are the time step size, the index of fractional derivative and space step size respectively. Numerical experiments are carried out to demonstrate the theoretical analysis.