A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions

Authors:
Xuan Zhao;Zhi-zhong Sun
Affiliations:
Department of Mathematics, Southeast University, Nanjing 210096, PR China;Department of Mathematics, Southeast University, Nanjing 210096, PR China
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

Combining order reduction approach and L1 discretization, a box-type scheme is presented for solving a class of fractional sub-diffusion equation with Neumann boundary conditions. A new inner product and corresponding norm with a Sobolev embedding inequality are introduced. A novel technique is applied in the proof of both stability and convergence. The global convergence order in maximum norm is O(@t^2^-^@a+h^2). The accuracy and efficiency of the scheme are checked by two numerical tests.