Solutions For Fractional Diffusion Equation By Using A Chebyshev Spectral Tau Method

Abstract

In this thesis, the solution of fractional Diffusion equation using spectral Tau method was successfully implemented in Caputo sense and Chebyshev polynomial of second kind subjected to recurrence relation. A numerical technique for solving new generalized fractional diffusion equations is presented. The spectral Tau method is extended to study this problem, where the derivatives were defined in the Caputo fractional sense. Some numerical examples are given to demonstrate the validity and applicability of the method. In examples, we give some exact solution between error estimation and other numerical methods. The obtained numerical results reveal that given method very good approximation than other methods. This method provides very efficiently a convergent series solution form with easily computable coefficients. The obtained results show that the spectral Tau method is very effective and convenient