A new class of unconditionally stable numerical methods based on Adams Moulton's methods with application to radiative Darcy-Forchheimer flow

Present contribution has consisted of a construction of a class of new shooting methods and application to Darcy Forchheimer fluid flow over the linearly stretching sheet under the influence of thermal radiations. Governing equations of the flow phenomena are presented in the form of partial differential equations, and these governing partial differential equations are reduced into ordinary differential equations. The final ordinary differential equations are resolved by the present given shooting method based on the class of Adam Moulton's techniques with the Gauss-Siedel iterative method. Since the system of the first-order differential is discretized by the Adam Moulton method with the Gauss-Siedel iterative method containing some unknown initial conditions, a shooting approach is employed for finding unknown initial conditions. Also, it is proved that the Adam Moulton methods using Gauss-Seidel iterative method are unconditionally stable for any system of differential equations. In additions to this, finite element simulations containing velocity profile, streamlines, temperature profile and temperature contours are deliberated with the help of graphs, and tables. Thus, the main aim of the current paper is to calculate the unique results for a coupling approach based on Adams Moulton's method for the boundary layer flow problem with the effect of heat transfer.