Purpose: The purpose of this paper is to use the Adomian decomposition method (ADM) for solving boundary value problems with dual solutions. Design/methodology/approach: The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific applications. In this work, the authors seek to determine the relative merits of the ADM in the context of several important nonlinear boundary value models characterized by the existence of dual solutions. Findings: The ADM is shown to readily solve specific nonlinear BVPs possessing more than one solution. The decomposition series solution of these models requires the calculation of the Adomian polynomials appropriate to the particular system nonlinearity. The authors show that the ADM solves these models for any analytic nonlinearity in a practical and straightforward manner. The conclusions are supported by several numerical examples arising in various scientific applications which admit dual solutions. Originality/value: This paper presents an accurate work for solving nonlinear BVPs that possess dual solutions. The authors have demonstrated the widespread applicability of the ADM for solving various forms of these nonlinear equations.

This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay between susceptible S, infected I, and recovered R populations. A new parametric solution to this model has been presented. Applying the Adomian decomposition method (ADM) allows for the attaining of highly accurate approximate solutions in the context of the SIR epidemic model. To validate the accuracy and robustness of the proposed approach, a numerical exploration is conducted, considering a diverse range of experimental parameters. This numerical analysis provides valuable insights into the sensitivity and responsiveness of the SIR epidemic model under varying conditions, contributing to the broader understanding of infectious disease dynamics. The interplay between theoretical formulation and numerical exploration establishes a comprehensive framework for studying the SIR model, with implications for refining our ability to predict and manage the spread of infectious diseases.