High-order compact difference scheme for the numerical solution of time fractional heat equations.
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.
Department of Mathematics, Fatih University, 34500 Istanbul, Turkey.
Ibrahim
I
Karatay
Department of Mathematics, Fatih University, 34500 Istanbul, Turkey.
Serife R
SR
Bayramoglu
D055641:Mathematical Concepts