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In this paper, we provide explicitly the Adomian polynomials (AP) for transcendental-hyperbolic functions in a linear functional and forced the convergence of inconsistent solution series when Adomian decomposition method (ADM) is deployed in related problems by nonlinear Shanks transform (NST). These were achievable by developing a theoretical background of AP for transcendental-hyperbolic functions based upon a thorough examination of the historical preceding of ADM. Application of the presented polynomials resulted to unreliable series solutions which was, however, upturned on using NST in the problems considered. This paper has unified the notion of modified AP for transcendental-hyperbolic nonlinear functions and its application to similar equations. It further presented a reliable technique that forced convergence in unpredictable and alternating series solutions that are obtain by ADM.

Transcendental-hyperbolic functions and their Adomian polynomials with numerical results facilitated by nonlinear shanks transform