A NOVEL SPECTRAL APPROXIMATION FOR THE TWO-DIMENSIONAL FRACTIONAL SUB-DIFFUSION PROBLEMS
Research Abstract
This paper reports a new numerical method that enables easy and convenient
discretization of a two-dimensional sub-diffusion equation with fractional derivatives
of any order. The suggested method is based on Jacobi tau spectral procedure together
with the Jacobi operational matrix for fractional derivatives, described in the Caputo
sense. Such approach has the advantage of reducing the problem to the solution of a
system of algebraic equations, which may then be solved by any standard numerical
technique. The validity and effectiveness of the method are demonstrated by solving
two numerical examples, which are presented in the form of tables and graphs to make
more easier comparisons with the exact solutions and the results obtained by other
methods.
Research Keywords
Two-dimensional fractional diffusion equations; Tau method; Shifted Jacobi polynomials; Operational matrix; Caputo derivative.