The improved residual power series method for a system of differential equations: a new semi-numerical method.

This paper presents the extension of Improved Residual Power Series Method (IRPSM) towards the system of ordinary differential equations (ODEs). The present system of ODEs is based on the thin film flow over an inclined planar surface. The proposed system is highly nonlinear. Additionally, some embedded factors are taken into the flow analysis in order to investigate the impacts of these parameters on the flow profiles. The method is coded in MATHEMATICA 12.0 software. The results of the present analysis show that the IRPSM has a fast convergence. The impacts of embedded parameters have been successfully investigated and have comparable effects on the flow profiles. Comparison of the present results with the results present in the literature has confirmed the validity of IRPSM. The IRPSM is also applicable to the systems of both linear and highly nonlinear ordinary and partial differential equations. [ABSTRACT FROM AUTHOR]