Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method

Abstract

In this paper, we examine a system of two coupled nonlinear differential equations that relates the concentrations of carbon dioxide CO\(_2\) and phenyl glycidyl ether in solution. This system is subject to a set of Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. We apply the Adomian decomposition method combined with the Duan–Rach modified recursion scheme to analytically treat this system of coupled nonlinear boundary value problems. The rapid convergence of our analytic approximate solutions is demonstrated by graphs of the objective error analysis instead of comparison to an alternate solution technique alone. The Adomian decomposition method yields a rapidly convergent, easily computable, and readily verifiable sequence of analytic approximate solutions that is suitable for numerical parametric simulations. Thus our sequence of approximate solutions are shown to identically satisfy the original set of model equations as closely as we please.