A Class of Unconditionally Stable Shooting Methods with Application to Radiative Darcy–Forchheimer Flow

Abstract

Since there are shooting methods in the literature to solve ordinary differential equations (ODEs), those are mainly based on Runge–Kutta explicit methods. It is a proven fact that explicit Runge–Kutta methods are conditionally stable. The present contribution consists of constructing a class of shooting methods based on implicit methods that are unconditionally stable with their application to solving the problem of Darcy–Forchheimer’s flow over the stretching sheet under the influence of thermal radiations. Governing equations of the flow phenomena are presented in the form of partial differential equations (PDEs). Further, these PDEs are reduced into ODEs which are tackled by the present constructing shooting methods based on the class of Adam Moulton’s techniques with the Gauss–Siedel iterative method. The stability and convergence for the system of differential equations are also given. Thus, the main advantage of the presented methods is to turn the implicit methods into explicit methods using the shooting approach. Also, the impact of inertia coefficient, porosity parameter, radiation parameter, and Prandtl number on velocity and temperature profiles is given graphically. It is seen that the increment of the porosity parameter escalates the temperature profile. A computational code for the proposed model scheme may be made available to readers upon request for convenience.