PICARD AND ADOMIAN DECOMPOSITION METHODS FOR A COUPLED SYSTEM OF QUADRATIC INTEGRAL EQUATIONS

A. M. A.  EL-SAYED; H. H. G.  HASHEM; E. A. A.   ZIADA

PICARD AND ADOMIAN DECOMPOSITION METHODS FOR A COUPLED SYSTEM OF QUADRATIC INTEGRAL EQUATIONS

Authors

A. M. A. EL-SAYED Faculty of Science, Alexandria University, Alexandria, Egypt
H. H. G. HASHEM Faculty of Science, Qassim University, Buraidah, Saudi Arabia
E. A. A. ZIADA Faculty of Engineering, Delta University for Science and Technology, Gamasa, Egypt

Keywords:

Coupled systems, Quadratic integral equation, Picard method, Adomian method, Continuous unique solution, Fractional-order integration, Convergence analysis, Error analysis

Abstract

The comparison between the classical method of successive approximations (Picard) method and Adomian decomposition method was studied in many papers for example ([15] and [37]). In this paper we are concerning with two analytical methods; the classical method of successive approximations (Picard) [18] and Adomian decomposition methods ([1]-[6], [16] and [17]) for a coupled system of quadratic integral equations of fractional order. Also, the existence and uniqueness of the solution and the convergence will be discussed for each method and some examples will be studied.