Solution of systems of algebraic equations by Adomian decomposition method

ABSTRACT MSc.Thesis SOLUTION OF SYSTEMS OF ALGEBRAIC EQUATIONS BY ADOMIAN DECOMPOSITION METHOD S. BATTAL GAZÎ KARAKOÇ inönü University Graduate School of Natural and Applied Sciences Department of Mathematics 92+viii pages 2006 Supervisor : Yrd. Doç. Dr. Sibel ÖZER This MSc. thesis consists of seven chapters. In the first chapter, some basic definitions and theorems to be used in the later chapter are outlined. In the second and third chapters, some solution methods of linear and nonlinear algebraic equation systems in literature are examined. In the fourth chapter, Adomian polinoms are computed for various nonlinear functions. In the fifth chapter, the solution of linear algebraic equation systems is given by using Adomian decomposition method. The obtained results have showed that this method and the results obtained from classical Jacobi iterativ methods are the same. In the sixth chapter, the solution of nonlinear algebraic equation systems is given by using Adomian decomposition method. It is understood that the obtained results are agreement with Basic iteration and Newton-Raphson methods. In the seventh chapter, the numerical results obtained in the sixth chapter are evaluated. KEYWORDS: Adomian decomposition method, Adomian polynomials, linear algebraic equation systems, nonlinear algebraic equation systems. IV