**4. Numerical Methods**

The governing ODEs are highly non-linear and, therefore, we adopt the numerical approach in order to solve Equations (11)–(14) and Equations (26)–(19). In this study, two methods have been employed, namely shooting method and Three-stage Lobatto III-A formula, which were used in many research articles of same authors previously [refer to 17,20,23,26]. The descriptions regarding these methods are explained below.
