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High-order compact difference scheme for the numerical solution of time fractional heat equations.

ABSTRACT: A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme.

SUBMITTER: Karatay I

PROVIDER: S-EPMC3947870 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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