Alla Tareq Balasim ¹, Norhashidah Hj. Mohd. Ali ¹

Affiliations
1 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MY

Abstract

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 45^o 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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