A compact finite difference scheme for the fractional sub-diffusion equations

Authors:
Guang-hua Gao;Zhi-zhong Sun
Affiliations:
Department of Mathematics, Southeast University, Nanjing 211189, People's Republic of China;Department of Mathematics, Southeast University, Nanjing 211189, People's Republic of China
Venue:
Journal of Computational Physics
Year:
2011

Citing 13
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Abstract

In this paper, a compact finite difference scheme for the fractional sub-diffusion equations is derived. After a transformation of the original problem, the L1 discretization is applied for the time-fractional part and fourth-order accuracy compact approximation for the second-order space derivative. The unique solvability of the difference solution is discussed. The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis. The technique is quite novel and different from previous analytical methods. Finally, a numerical example is provided to show the effectiveness and accuracy of the method.