Determination of the Correct Range of Physical Parameters in the Approximate Analytical Solutions of Nonlinear Equations Using the Adomian Decomposition Method

Physical parameters in dimensionless form in the governing equations of real-life phenomena naturally occur. How to control them by determining their range of validity is in general a big issue. In this paper, a mathematical approach is presented to identify the correct range of physical parameters adopting the recently popular analytic approximate Adomian decomposition method (ADM). Having found the approximate analytical Adomian series solution up to a specified truncation order, the squared residual error formula is employed to work out the threshold and the existence domain of certain physical parameters satisfying a preassigned tolerance. If the current procedure is not closely pursued, the presented results with the ADM may not be up to the desired level of accuracy (the worst is the divergent physically meaningless solutions), or much more ADM series terms need to be computed to satisfy certain accuracy. Examples reveal the necessity of the present approach to make sure that the results embark the correct range of physical parameters in the study of a physical problem containing several dominating parameters.