High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations

Abstract EN

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.