A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations

Abstract

In this article, we study some fundamental results concerning the convergence of the Adomian decomposition method (ADM) for an abstract Cauchy problem of a system of first-order nonlinear differential equations. Under certain conditions, we obtain upper estimates for the norm of solutions of this system. We also obtain results about the error estimates for the approximate solutions by the ADM and discuss their applications.

Keywords:

• coupled system of nonlinear first-order differential equations
• Adomian decomposition method
• Adomian polynomials

2000 AMS Subject Classifications:

• 12H20
• 93C25
• 93C15
• 93C10
• 93C23