Indian Journal of Science and Technology

The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Alternatively, you can download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link above.

Fullscreen Fullscreen Off


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.
User