A new class of unconditionally stable numerical methods based on Adams
Moulton's methods with application to radiative Darcy-Forchheimer flow
- Yasir Nawaz,
- Muhammad Arif
Abstract
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.