Indian Journal of Science and Technology
Year: 2015, Volume: 8, Issue: 32, Pages: 1-7
Alla Tareq Balasim* and Norhashidah Hj. Mohd. Ali
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia; [email protected], [email protected]
This paper aims to examine the effectiveness of a rotated iterative method to solve the two-dimensional time fractional diffusion equations which are used when describing transport processes with long memory where the rate of diffusion is inconsistent with the classical Brownian motion model. This type of equation is obtained by replacing the first order time derivative in the standard diffusion equation with a fractional derivative of order α, where 0 < α < 1, in accordance with Riemann-Liouville or Caputo. The developed method is derived from the Standard Crank-Nicolson (S(C-N)) scheme by rotating clockwise 45o with respect to the standard mesh. The study demonstrates the enhanced efficiency and superiority of the Rotated Crank-Nicolson (R(C-N)) method which overall reduces the CPU consumption time.
Keywords: Caputo’s Fractional Derivative, Crank-Nicolson Schemes, Diffusion Equation, Gauss–Seidel Method, Rotated Crank-Nicolson Schemes, Time Fractional
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