The ANZIAM Journal

Research Article

A CHEBYSHEV PSEUDO-SPECTRAL METHOD FOR SOLVING FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

N. H. SWEILAMa1 c1 and M. M. KHADERa2

a1 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt (email: n_sweilam@yahoo.com)

a2 Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt (email: mohamedmbd@yahoo.com)

Abstract

A Chebyshev pseudo-spectral method for solving numerically linear and nonlinear fractional-order integro-differential equations of Volterra type is considered. The fractional derivative is described in the Caputo sense. The suggested method reduces these types of equations to the solution of linear or nonlinear algebraic equations. Special attention is given to study the convergence of the proposed method. Finally, some numerical examples are provided to show that this method is computationally efficient, and a comparison is made with existing results.

(Received March 23 2010)

(Revised August 13 2010)

(Online publication November 04 2010)

2000 Mathematics subject classification

  • primary 26A33

Keywords and phrases

  • Chebyshev pseudo-spectral method;
  • fractional-order integro-differential equations of Volterra type

Correspondence:

c1 For correspondence; e-mail: n˙sweilam@yahoo.com