In this paper, a method based on the Tau method with arbitrary bases is developed to find the numerical solution of Fredholm integro-differential equations; the differential part appearing in the equation is replaced by its operational Tau representation. Some numerical results are given to demonstrate the superior performance of the Tau method, particularly, with the Chebyshev and Legendre bas...

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials ar...

The Tau method, produces approximate polynomial solution of differential, integral and integro-differential equations (see [E.l,Ortiz, The Tau method, SIAM J. Numer. Anal. 6 (3) (1969) 480–492; E.l. Ortiz, H. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing 27 (1981) 15–25; S.M. Hosseini, S. Shahmorad, A matrix formulat...

The principle result of this paper is the following operational Tau method based upon Müntz-Legendre polynomials. This methodology provides a computational technique for numerical solution of fractional differential equations by using a sequence of matrix operations. The main property of Müntz polynomials is that fractional derivatives of these polynomials can be expressed in terms of the same ...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper a novel approach based on the homotopy analysis method (HAM) is presented for solving nonlinea...

In this paper, numerical technique based on monic Laguerre polynomials is proposed to obtain approximate solutions of initial value problems for systems fractional order integro-differential equations (FIDEs). Operational integral matrix constructed. This operational applied together with the Tau method solve FIDEs. FIDEs will be transformed into a system algebraic which can solved easily. Nume...